diff --git a/docs/release_notes/release_notes-0.15.0.rst b/docs/release_notes/release_notes-0.15.0.rst
index d273aaf6ae0..9135a41de5d 100644
--- a/docs/release_notes/release_notes-0.15.0.rst
+++ b/docs/release_notes/release_notes-0.15.0.rst
@@ -30,6 +30,7 @@ Key Features and Updates
   * FIX-#4531: Fix a makedirs race condition in to_parquet (#4533)
   * FIX-#4464: Refactor Ray utils and quick fix groupby.count failing on virtual partitions (#4490)
   * FIX-#4436: Fix to_pydatetime dtype for timezone None (#4437)
+  * FIX-#4541: Fix merge_asof with non-unique right index (#4542)
 * Performance enhancements
   * FEAT-#4320: Add connectorx as an alternative engine for read_sql (#4346)
   * PERF-#4493: Use partition size caches more in Modin dataframe (#4495)
diff --git a/modin/pandas/general.py b/modin/pandas/general.py
index 79bf90f5809..1d29ae63594 100644
--- a/modin/pandas/general.py
+++ b/modin/pandas/general.py
@@ -194,6 +194,11 @@ def merge_asof(
         or not isinstance(by, (str, type(None)))
         or not isinstance(left_by, (str, type(None)))
         or not isinstance(right_by, (str, type(None)))
+        # The implementation below assumes that the right index is unique
+        # because it uses merge_asof to map each position in the merged
+        # index to the label of the one right row that should be merged
+        # at that row position.
+        or not right.index.is_unique
     ):
         if isinstance(right, DataFrame):
             right = to_pandas(right)
diff --git a/modin/pandas/test/test_general.py b/modin/pandas/test/test_general.py
index 7707c3ed518..4867e418a84 100644
--- a/modin/pandas/test/test_general.py
+++ b/modin/pandas/test/test_general.py
@@ -201,9 +201,12 @@ def test_merge_ordered():
         pd.merge_ordered(data_a, data_b, fill_method="ffill", left_by="group")
 
 
-def test_merge_asof():
+@pytest.mark.parametrize("right_index", [None, [0] * 5], ids=["default", "non_unique"])
+def test_merge_asof(right_index):
     left = pd.DataFrame({"a": [1, 5, 10], "left_val": ["a", "b", "c"]})
-    right = pd.DataFrame({"a": [1, 2, 3, 6, 7], "right_val": [1, 2, 3, 6, 7]})
+    right = pd.DataFrame(
+        {"a": [1, 2, 3, 6, 7], "right_val": [1, 2, 3, 6, 7]}, index=right_index
+    )
 
     with warns_that_defaulting_to_pandas():
         df = pd.merge_asof(left, right, on="a")