diff --git a/src/_pytest/python_api.py b/src/_pytest/python_api.py
index c64587bb219..81799552f3f 100644
--- a/src/_pytest/python_api.py
+++ b/src/_pytest/python_api.py
@@ -242,6 +242,19 @@ def _repr_compare(self, other_side: Mapping[object, float]) -> list[str]:
                 f"Lengths: {len(self.expected)} and {len(other_side)}",
             ]
 
+        # Check if keys match
+        expected_keys = set(self.expected.keys())
+        other_keys = set(other_side.keys())
+        if expected_keys != other_keys:
+            expected_only = expected_keys - other_keys
+            other_only = other_keys - expected_keys
+            msg = ["Dictionaries have different keys."]
+            if expected_only or other_only:
+                msg.append(
+                    f"Expected keys: {sorted(expected_keys)}, Actual keys: {sorted(other_keys)}"
+                )
+            return msg
+
         approx_side_as_map = {
             k: self._approx_scalar(v) for k, v in self.expected.items()
         }
diff --git a/testing/test_approx_dict_keys_13816.py b/testing/test_approx_dict_keys_13816.py
new file mode 100644
index 00000000000..e25433f8991
--- /dev/null
+++ b/testing/test_approx_dict_keys_13816.py
@@ -0,0 +1,54 @@
+"""Test for issue #13816 - better error messages for dict key mismatches in pytest.approx()"""
+
+from __future__ import annotations
+
+import pytest
+
+
+def test_approx_dicts_with_different_keys_clear_error():
+    """Test that pytest.approx() gives a clear error when dict keys don't match."""
+    expected = {"a": 1, "c": 3}
+    actual = {"a": 1, "b": 4}
+
+    with pytest.raises(AssertionError) as exc_info:
+        assert pytest.approx(actual) == expected
+
+    error_message = str(exc_info.value)
+    # Should mention "different keys" clearly
+    assert "different keys" in error_message.lower()
+    # Should NOT have the confusing KeyError message
+    assert "KeyError" not in error_message
+    # Should NOT mention "faulty __repr__"
+    assert "faulty __repr__" not in error_message
+
+
+def test_approx_dicts_with_extra_key_in_expected():
+    """Test error message when expected has extra keys."""
+    expected = {"a": 1, "b": 2, "c": 3}
+    actual = {"a": 1, "b": 2}
+
+    with pytest.raises(AssertionError) as exc_info:
+        assert pytest.approx(actual) == expected
+
+    error_message = str(exc_info.value)
+    assert "different keys" in error_message.lower()
+
+
+def test_approx_dicts_with_extra_key_in_actual():
+    """Test error message when actual has extra keys."""
+    expected = {"a": 1, "b": 2}
+    actual = {"a": 1, "b": 2, "c": 3}
+
+    with pytest.raises(AssertionError) as exc_info:
+        assert pytest.approx(actual) == expected
+
+    error_message = str(exc_info.value)
+    assert "different keys" in error_message.lower()
+
+
+def test_approx_dicts_matching_keys_still_works():
+    """Test that dicts with matching keys still work normally."""
+    expected = {"a": 1.0001, "b": 2.0001}
+    actual = {"a": 1.0, "b": 2.0}
+
+    assert pytest.approx(actual, rel=1e-3) == expected