diff --git a/datafusion/functions-aggregate/src/approx_median.rs b/datafusion/functions-aggregate/src/approx_median.rs
index 575f31864c281..2598ce400a6d2 100644
--- a/datafusion/functions-aggregate/src/approx_median.rs
+++ b/datafusion/functions-aggregate/src/approx_median.rs
@@ -13,7 +13,7 @@ use std::sync::Arc;
 
 use datafusion_common::{Result, not_impl_err};
 use datafusion_expr::function::{AccumulatorArgs, StateFieldsArgs};
-use datafusion_expr::utils::format_state_name;
+use datafusion_expr::utils::{AggregateOrderSensitivity, format_state_name};
 use datafusion_expr::{
     Accumulator, AggregateUDFImpl, Coercion, Documentation, Signature, TypeSignature,
     TypeSignatureClass, Volatility,
@@ -137,6 +137,10 @@ impl AggregateUDFImpl for ApproxMedian {
         }
     }
 
+    fn order_sensitivity(&self) -> AggregateOrderSensitivity {
+        AggregateOrderSensitivity::Insensitive
+    }
+
     fn documentation(&self) -> Option<&Documentation> {
         self.doc()
     }
diff --git a/datafusion/sqllogictest/test_files/aggregate.slt b/datafusion/sqllogictest/test_files/aggregate.slt
index 1e12ee4194a49..d085ec35e9113 100644
--- a/datafusion/sqllogictest/test_files/aggregate.slt
+++ b/datafusion/sqllogictest/test_files/aggregate.slt
@@ -759,6 +759,14 @@ SELECT approx_median(c12) FROM aggregate_test_100
 statement error
 SELECT approx_median(c1) FROM aggregate_test_100
 
+# APPROX_MEDIAN ignores aggregate ORDER BY keys. They must not be interpreted
+# as percentile arguments by the shared accumulator.
+query R
+SELECT approx_median(x ORDER BY k)
+FROM (VALUES (1.0, 3), (2.0, 1), (3.0, 2)) t(x, k)
+----
+2
+
 # csv_query_median_1
 query R
 SELECT median(c2) FROM aggregate_test_100