diff --git a/CHANGELOG.md b/CHANGELOG.md
index b1c6fab317..65f665d4f0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -49,6 +49,7 @@
 * [BUGFIX] Distributor: return HTTP status 415 Unsupported Media Type instead of 200 Success for Remote Write 2.0 until we support it. #10423
 * [BUGFIX] Query-frontend: Add flag `-query-frontend.prom2-range-compat` and corresponding YAML to rewrite queries with ranges that worked in Prometheus 2 but are invalid in Prometheus 3. #10445 #10461 #10502
 * [BUGFIX] Distributor: Fix edge case at the HA-tracker with memberlist as KVStore, where when a replica in the KVStore is marked as deleted but not yet removed, it fails to update the KVStore. #10443
+* [BUGFIX] Distributor: Fix panics in `DurationWithJitter` util functions when computed variance is zero. #10507
 * [BUGFIX] Ingester: Fixed a race condition in the `PostingsForMatchers` cache that may have infrequently returned expired cached postings. #10500
 
 ### Mixin
diff --git a/pkg/util/time.go b/pkg/util/time.go
index 4b93313f52..800412a4b5 100644
--- a/pkg/util/time.go
+++ b/pkg/util/time.go
@@ -66,12 +66,11 @@ func ParseDurationMS(s string) (int64, error) {
 
 // DurationWithJitter returns random duration from "input - input*variance" to "input + input*variance" interval.
 func DurationWithJitter(input time.Duration, variancePerc float64) time.Duration {
-	// No duration? No jitter.
-	if input == 0 {
+	variance := int64(float64(input) * variancePerc)
+	if variance <= 0 {
 		return 0
 	}
 
-	variance := int64(float64(input) * variancePerc)
 	jitter := rand.Int63n(variance*2) - variance
 
 	return input + time.Duration(jitter)
@@ -79,12 +78,11 @@ func DurationWithJitter(input time.Duration, variancePerc float64) time.Duration
 
 // DurationWithPositiveJitter returns random duration from "input" to "input + input*variance" interval.
 func DurationWithPositiveJitter(input time.Duration, variancePerc float64) time.Duration {
-	// No duration? No jitter.
-	if input == 0 {
+	variance := int64(float64(input) * variancePerc)
+	if variance <= 0 {
 		return 0
 	}
 
-	variance := int64(float64(input) * variancePerc)
 	jitter := rand.Int63n(variance)
 
 	return input + time.Duration(jitter)
@@ -92,12 +90,11 @@ func DurationWithPositiveJitter(input time.Duration, variancePerc float64) time.
 
 // DurationWithNegativeJitter returns random duration from "input - input*variance" to "input" interval.
 func DurationWithNegativeJitter(input time.Duration, variancePerc float64) time.Duration {
-	// No duration? No jitter.
-	if input == 0 {
+	variance := int64(float64(input) * variancePerc)
+	if variance <= 0 {
 		return 0
 	}
 
-	variance := int64(float64(input) * variancePerc)
 	jitter := rand.Int63n(variance)
 
 	return input - time.Duration(jitter)
diff --git a/pkg/util/time_test.go b/pkg/util/time_test.go
index 60a5d66380..e06f328e0e 100644
--- a/pkg/util/time_test.go
+++ b/pkg/util/time_test.go
@@ -68,10 +68,6 @@ func TestDurationWithJitter(t *testing.T) {
 	}
 }
 
-func TestDurationWithJitter_ZeroInputDuration(t *testing.T) {
-	assert.Equal(t, time.Duration(0), DurationWithJitter(time.Duration(0), 0.5))
-}
-
 func TestDurationWithPositiveJitter(t *testing.T) {
 	const numRuns = 1000
 
@@ -82,10 +78,6 @@ func TestDurationWithPositiveJitter(t *testing.T) {
 	}
 }
 
-func TestDurationWithPositiveJitter_ZeroInputDuration(t *testing.T) {
-	assert.Equal(t, time.Duration(0), DurationWithPositiveJitter(time.Duration(0), 0.5))
-}
-
 func TestDurationWithNegativeJitter(t *testing.T) {
 	const numRuns = 1000
 
@@ -96,8 +88,16 @@ func TestDurationWithNegativeJitter(t *testing.T) {
 	}
 }
 
-func TestDurationWithNegativeJitter_ZeroInputDuration(t *testing.T) {
-	assert.Equal(t, time.Duration(0), DurationWithNegativeJitter(time.Duration(0), 0.5))
+func TestDurationWithJitterFamily_ZeroOutputs(t *testing.T) {
+	// Make sure all of these functions return zero when the computed variance is <= 0.
+
+	type durFunc func(time.Duration, float64) time.Duration
+	for _, f := range []durFunc{DurationWithJitter, DurationWithNegativeJitter, DurationWithPositiveJitter} {
+		assert.Equal(t, time.Duration(0), f(time.Duration(0), 0.5))
+		assert.Equal(t, time.Duration(0), f(time.Duration(7), 0.1))
+		assert.Equal(t, time.Duration(0), f(time.Duration(7), -0.1))
+		assert.Equal(t, time.Duration(0), f(10*time.Minute, -0.1))
+	}
 }
 
 func TestParseTime(t *testing.T) {