diff --git a/ci/conda_env_cpp.txt b/ci/conda_env_cpp.txt
index f7e7c3ce1c1d7..2e7b568fc53cd 100644
--- a/ci/conda_env_cpp.txt
+++ b/ci/conda_env_cpp.txt
@@ -16,11 +16,12 @@
 # under the License.
 
 aws-sdk-cpp=1.11.68
-azure-core-cpp=1.10.3
-azure-identity-cpp=1.6.0
-azure-storage-blobs-cpp=12.10.0
-azure-storage-common-cpp=12.5.0
-azure-storage-files-datalake-cpp=12.9.0
+# There is a problem with the 1.11.0 conda release of azure-core-cpp https://github.com/conda-forge/admin-requests/pull/911
+azure-core-cpp>=1.10.3,<1.11.0
+azure-identity-cpp>=1.6.0
+azure-storage-blobs-cpp>=12.10.0
+azure-storage-common-cpp>=12.5.0
+azure-storage-files-datalake-cpp>=12.9.0
 benchmark>=1.6.0
 boost-cpp>=1.68.0
 brotli