diff --git a/docs/release-notes/0.10.9.md b/docs/release-notes/0.10.9.md
index 55948a2a1..519704b3a 100644
--- a/docs/release-notes/0.10.9.md
+++ b/docs/release-notes/0.10.9.md
@@ -9,6 +9,7 @@
 * Upper bound {mod}`numpy` for `gpu` installation on account of {issue}`cupy/cupy#8391` {pr}`1540` {user}`ilan-gold`
 * Fix writing large number of columns for `h5` files {pr}`1147` {user}`ilan-gold` {user}`selmanozleyen`
 * Upper bound dask on account of {issue}`1579` {pr}`1580` {user}`ilan-gold`
+* Disallow using {class}`~pandas.DataFrame`s with multi-index columns {pr}`1589` {user}`ilan-gold`
 * Ensure setting {attr}`pandas.DataFrame.index` on a view of a {class}`~anndata.AnnData` instantiates the {class}`~pandas.DataFrame` from the view {pr}`1586` {user}`ilan-gold`
 
 #### Documentation
diff --git a/src/anndata/_core/aligned_mapping.py b/src/anndata/_core/aligned_mapping.py
index 26c89d9f2..e2f6e4352 100644
--- a/src/anndata/_core/aligned_mapping.py
+++ b/src/anndata/_core/aligned_mapping.py
@@ -13,7 +13,13 @@
 
 from .._warnings import ExperimentalFeatureWarning, ImplicitModificationWarning
 from ..compat import AwkArray
-from ..utils import axis_len, convert_to_dict, deprecated, warn_once
+from ..utils import (
+    axis_len,
+    convert_to_dict,
+    deprecated,
+    raise_value_error_if_multiindex_columns,
+    warn_once,
+)
 from .access import ElementRef
 from .index import _subset
 from .storage import coerce_array
@@ -258,16 +264,18 @@ def to_df(self) -> pd.DataFrame:
         return df
 
     def _validate_value(self, val: Value, key: str) -> Value:
-        if isinstance(val, pd.DataFrame) and not val.index.equals(self.dim_names):
-            # Could probably also re-order index if it’s contained
-            try:
-                pd.testing.assert_index_equal(val.index, self.dim_names)
-            except AssertionError as e:
-                msg = f"value.index does not match parent’s {self.dim} names:\n{e}"
-                raise ValueError(msg) from None
-            else:
-                msg = "Index.equals and pd.testing.assert_index_equal disagree"
-                raise AssertionError(msg)
+        if isinstance(val, pd.DataFrame):
+            raise_value_error_if_multiindex_columns(val, f"{self.attrname}[{key!r}]")
+            if not val.index.equals(self.dim_names):
+                # Could probably also re-order index if it’s contained
+                try:
+                    pd.testing.assert_index_equal(val.index, self.dim_names)
+                except AssertionError as e:
+                    msg = f"value.index does not match parent’s {self.dim} names:\n{e}"
+                    raise ValueError(msg) from None
+                else:
+                    msg = "Index.equals and pd.testing.assert_index_equal disagree"
+                    raise AssertionError(msg)
         return super()._validate_value(val, key)
 
     @property
diff --git a/src/anndata/_core/anndata.py b/src/anndata/_core/anndata.py
index 7da29e4a4..49d47665d 100644
--- a/src/anndata/_core/anndata.py
+++ b/src/anndata/_core/anndata.py
@@ -26,7 +26,12 @@
 from .._settings import settings
 from ..compat import DaskArray, SpArray, ZarrArray, _move_adj_mtx
 from ..logging import anndata_logger as logger
-from ..utils import axis_len, deprecated, ensure_df_homogeneous
+from ..utils import (
+    axis_len,
+    deprecated,
+    ensure_df_homogeneous,
+    raise_value_error_if_multiindex_columns,
+)
 from .access import ElementRef
 from .aligned_df import _gen_dataframe
 from .aligned_mapping import AlignedMappingProperty, AxisArrays, Layers, PairwiseArrays
@@ -231,9 +236,13 @@ def __init__(
         *,
         obsp: np.ndarray | Mapping[str, Sequence[Any]] | None = None,
         varp: np.ndarray | Mapping[str, Sequence[Any]] | None = None,
-        oidx: Index1D = None,
-        vidx: Index1D = None,
+        oidx: Index1D | None = None,
+        vidx: Index1D | None = None,
     ):
+        # check for any multi-indices that aren’t later checked in coerce_array
+        for attr, key in [(obs, "obs"), (var, "var"), (X, "X")]:
+            if isinstance(attr, pd.DataFrame):
+                raise_value_error_if_multiindex_columns(attr, key)
         if asview:
             if not isinstance(X, AnnData):
                 raise ValueError("`X` has to be an AnnData object.")
@@ -733,9 +742,10 @@ def n_vars(self) -> int:
         """Number of variables/features."""
         return len(self.var_names)
 
-    def _set_dim_df(self, value: pd.DataFrame, attr: str):
+    def _set_dim_df(self, value: pd.DataFrame, attr: Literal["obs", "var"]):
         if not isinstance(value, pd.DataFrame):
             raise ValueError(f"Can only assign pd.DataFrame to {attr}.")
+        raise_value_error_if_multiindex_columns(value, attr)
         value_idx = self._prep_dim_index(value.index, attr)
         if self.is_view:
             self._init_as_actual(self.copy())
diff --git a/src/anndata/_core/storage.py b/src/anndata/_core/storage.py
index bc6a091d3..15630122f 100644
--- a/src/anndata/_core/storage.py
+++ b/src/anndata/_core/storage.py
@@ -20,7 +20,11 @@
     ZappyArray,
     ZarrArray,
 )
-from ..utils import ensure_df_homogeneous, join_english
+from ..utils import (
+    ensure_df_homogeneous,
+    join_english,
+    raise_value_error_if_multiindex_columns,
+)
 from .sparse_dataset import BaseCompressedSparseDataset
 
 if TYPE_CHECKING:
@@ -84,6 +88,8 @@ def coerce_array(
             value = value.A
         return value
     if isinstance(value, pd.DataFrame):
+        if allow_df:
+            raise_value_error_if_multiindex_columns(value, name)
         return value if allow_df else ensure_df_homogeneous(value, name)
     # if value is an array-like object, try to convert it
     e = None
diff --git a/src/anndata/tests/helpers.py b/src/anndata/tests/helpers.py
index 6a30f4c32..185808b8d 100644
--- a/src/anndata/tests/helpers.py
+++ b/src/anndata/tests/helpers.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import itertools
 import random
 import re
 import warnings
@@ -1000,3 +1001,13 @@ def __init__(self, *_args, **_kwargs) -> None:
             raise ImportError(
                 "zarr must be imported to create an `AccessTrackingStore` instance."
             )
+
+
+def get_multiindex_columns_df(shape):
+    return pd.DataFrame(
+        np.random.rand(shape[0], shape[1]),
+        columns=pd.MultiIndex.from_tuples(
+            list(itertools.product(["a"], range(shape[1] - (shape[1] // 2))))
+            + list(itertools.product(["b"], range(shape[1] // 2)))
+        ),
+    )
diff --git a/src/anndata/utils.py b/src/anndata/utils.py
index 177115d26..3ff844054 100644
--- a/src/anndata/utils.py
+++ b/src/anndata/utils.py
@@ -400,3 +400,12 @@ def is_hidden(attr) -> bool:
             for item in type.__dir__(cls)
             if not is_hidden(getattr(cls, item, None))
         ]
+
+
+def raise_value_error_if_multiindex_columns(df: pd.DataFrame, attr: str):
+    if isinstance(df.columns, pd.MultiIndex):
+        msg = (
+            "MultiIndex columns are not supported in AnnData. "
+            f"Please use a single-level index for {attr}."
+        )
+        raise ValueError(msg)
diff --git a/tests/test_annot.py b/tests/test_annot.py
index 7f4c2697e..8287add0d 100644
--- a/tests/test_annot.py
+++ b/tests/test_annot.py
@@ -8,6 +8,7 @@
 from natsort import natsorted
 
 import anndata as ad
+from anndata.tests.helpers import get_multiindex_columns_df
 
 
 @pytest.mark.parametrize("dtype", [object, "string"])
@@ -63,3 +64,10 @@ def test_non_str_to_not_categorical():
     result_non_transformed = adata.obs.drop(columns=["str_with_nan"])
 
     pd.testing.assert_frame_equal(expected_non_transformed, result_non_transformed)
+
+
+def test_error_multiindex():
+    adata = ad.AnnData(np.random.rand(100, 10))
+    df = get_multiindex_columns_df((adata.shape[0], 20))
+    with pytest.raises(ValueError, match=r"MultiIndex columns are not supported"):
+        adata.obs = df
diff --git a/tests/test_base.py b/tests/test_base.py
index 02e4eabe1..277e8c8ab 100644
--- a/tests/test_base.py
+++ b/tests/test_base.py
@@ -14,7 +14,7 @@
 from anndata import AnnData, ImplicitModificationWarning
 from anndata._settings import settings
 from anndata.compat import CAN_USE_SPARSE_ARRAY
-from anndata.tests.helpers import assert_equal, gen_adata
+from anndata.tests.helpers import assert_equal, gen_adata, get_multiindex_columns_df
 
 # some test objects that we use below
 adata_dense = AnnData(np.array([[1, 2], [3, 4]]))
@@ -117,6 +117,14 @@ def test_create_from_df():
     assert df.index.tolist() == ad.obs_names.tolist()
 
 
+@pytest.mark.parametrize("attr", ["X", "obs", "obsm"])
+def test_error_create_from_multiindex_df(attr):
+    df = get_multiindex_columns_df((100, 20))
+    val = df if attr != "obsm" else {"df": df}
+    with pytest.raises(ValueError, match=r"MultiIndex columns are not supported"):
+        AnnData(**{attr: val}, shape=(100, 10))
+
+
 def test_create_from_sparse_df():
     s = sp.random(20, 30, density=0.2)
     obs_names = [f"obs{i}" for i in range(20)]
diff --git a/tests/test_obsmvarm.py b/tests/test_obsmvarm.py
index 63fbc9bc6..91516de2f 100644
--- a/tests/test_obsmvarm.py
+++ b/tests/test_obsmvarm.py
@@ -7,6 +7,7 @@
 from scipy import sparse
 
 from anndata import AnnData
+from anndata.tests.helpers import get_multiindex_columns_df
 
 M, N = (100, 100)
 
@@ -137,3 +138,9 @@ def test_shape_error(adata: AnnData):
         ),
     ):
         adata.obsm["b"] = np.zeros((adata.shape[0] + 1, adata.shape[0]))
+
+
+def test_error_set_multiindex_df(adata: AnnData):
+    df = get_multiindex_columns_df((adata.shape[0], 20))
+    with pytest.raises(ValueError, match=r"MultiIndex columns are not supported"):
+        adata.obsm["df"] = df