diff --git a/pandas/core/arrays/boolean.py b/pandas/core/arrays/boolean.py
index a5109ab17af70..10e695c1e221d 100644
--- a/pandas/core/arrays/boolean.py
+++ b/pandas/core/arrays/boolean.py
@@ -378,7 +378,7 @@ def _logical_method(self, other, op):  # type: ignore[override]
         elif is_list_like(other):
             other = np.asarray(other, dtype="bool")
             if other.ndim > 1:
-                raise NotImplementedError("can only perform ops with 1-d structures")
+                return NotImplemented
             other, mask = coerce_to_array(other, copy=False)
         elif isinstance(other, np.bool_):
             other = other.item()
diff --git a/pandas/tests/arithmetic/test_numeric.py b/pandas/tests/arithmetic/test_numeric.py
index 9fc148f492e48..c6d48aac1a441 100644
--- a/pandas/tests/arithmetic/test_numeric.py
+++ b/pandas/tests/arithmetic/test_numeric.py
@@ -862,6 +862,19 @@ def test_modulo_zero_int(self):
             expected = Series([np.nan, 0.0])
             tm.assert_series_equal(result, expected)
 
+    def test_non_1d_ea_raises_notimplementederror(self):
+        # GH#61866
+        ea_array = array([1, 2, 3, 4, 5], dtype="Int64").reshape(5, 1)
+        np_array = np.array([1, 2, 3, 4, 5], dtype=np.int64).reshape(5, 1)
+
+        msg = "can only perform ops with 1-d structures"
+
+        with pytest.raises(NotImplementedError, match=msg):
+            ea_array * np_array
+
+        with pytest.raises(NotImplementedError, match=msg):
+            np_array * ea_array
+
 
 class TestAdditionSubtraction:
     # __add__, __sub__, __radd__, __rsub__, __iadd__, __isub__