diff --git a/bigframes/dataframe.py b/bigframes/dataframe.py
index c9df349556..7f7268a9d5 100644
--- a/bigframes/dataframe.py
+++ b/bigframes/dataframe.py
@@ -3924,6 +3924,10 @@ def map(self, func, na_action: Optional[str] = None) -> DataFrame:
         )
 
     def apply(self, func, *, axis=0, args: typing.Tuple = (), **kwargs):
+        # In Bigframes remote function, DataFrame '.apply' method is specifically
+        # designed to work with row-wise or column-wise operations, where the input
+        # to the applied function should be a Series, not a scalar.
+
         if utils.get_axis_number(axis) == 1:
             msg = "axis=1 scenario is in preview."
             warnings.warn(msg, category=bfe.PreviewWarning)
@@ -4031,8 +4035,19 @@ def apply(self, func, *, axis=0, args: typing.Tuple = (), **kwargs):
 
             return result_series
 
+        # At this point column-wise or element-wise remote function operation will
+        # be performed (not supported).
+        if hasattr(func, "bigframes_remote_function"):
+            raise NotImplementedError(
+                "BigFrames DataFrame '.apply()' does not support remote function "
+                "for column-wise (i.e. with axis=0) operations, please use a "
+                "regular python function instead. For element-wise operations of "
+                "the remote function, please use '.map()'."
+            )
+
         # Per-column apply
         results = {name: func(col, *args, **kwargs) for name, col in self.items()}
+
         if all(
             [
                 isinstance(val, bigframes.series.Series) or utils.is_list_like(val)
diff --git a/tests/system/small/test_remote_function.py b/tests/system/small/test_remote_function.py
index 808bf1c055..c3f3890459 100644
--- a/tests/system/small/test_remote_function.py
+++ b/tests/system/small/test_remote_function.py
@@ -968,6 +968,30 @@ def test_read_gbq_function_supported_python_output_type(
     rf.read_gbq_function(str(sql_routine.reference), session=session)
 
 
+@pytest.mark.flaky(retries=2, delay=120)
+def test_df_apply_scalar_func(session, scalars_dfs):
+    scalars_df, _ = scalars_dfs
+    bdf = bigframes.pandas.DataFrame(
+        {
+            "Column1": scalars_df["string_col"],
+            "Column2": scalars_df["string_col"],
+        }
+    )
+
+    # The "cw_lower_case_ascii_only" is a scalar function.
+    func_ref = session.read_gbq_function("bqutil.fn.cw_lower_case_ascii_only")
+
+    # DataFrame '.apply()' only supports series level application.
+    with pytest.raises(NotImplementedError) as context:
+        bdf.apply(func_ref)
+    assert str(context.value) == (
+        "BigFrames DataFrame '.apply()' does not support remote function for "
+        "column-wise (i.e. with axis=0) operations, please use a regular python "
+        "function instead. For element-wise operations of the remote function, "
+        "please use '.map()'."
+    )
+
+
 @pytest.mark.flaky(retries=2, delay=120)
 def test_read_gbq_function_multiple_inputs_not_a_row_processor(session):
     with pytest.raises(ValueError) as context: