diff --git a/doc/releases/changelog-dev.md b/doc/releases/changelog-dev.md
index 7c259a4d363..2a70356a3ca 100644
--- a/doc/releases/changelog-dev.md
+++ b/doc/releases/changelog-dev.md
@@ -122,9 +122,11 @@
 * `qml.matrix()` called on the following will raise an error if `wire_order` is not specified:
   * tapes with more than one wire.
   * quantum functions.
+  * Operator class where ``num_wires`` does not equal to 1
   * QNodes if the device does not have wires specified.
   * PauliWords and PauliSentences with more than one wire.
   [(#5328)](https://github.com/PennyLaneAI/pennylane/pull/5328)
+  [(#5359)](https://github.com/PennyLaneAI/pennylane/pull/5359)
 
 * ``qml.pauli.pauli_mult`` and ``qml.pauli.pauli_mult_with_phase`` are now removed. Instead, you  should use ``qml.simplify(qml.prod(pauli_1, pauli_2))`` to get the reduced operator.
   [(#5324)](https://github.com/PennyLaneAI/pennylane/pull/5324)
diff --git a/pennylane/ops/functions/matrix.py b/pennylane/ops/functions/matrix.py
index cd3681eb1ec..37cb1bc1df7 100644
--- a/pennylane/ops/functions/matrix.py
+++ b/pennylane/ops/functions/matrix.py
@@ -200,7 +200,7 @@ def circuit():
                 )
 
         elif callable(op):
-            if wire_order is None:
+            if getattr(op, "num_wires", 0) != 1 and wire_order is None:
                 raise ValueError("wire_order is required by qml.matrix() for quantum functions.")
 
         else:
diff --git a/tests/ops/functions/test_matrix.py b/tests/ops/functions/test_matrix.py
index 0462a3447f9..f84229d6b35 100644
--- a/tests/ops/functions/test_matrix.py
+++ b/tests/ops/functions/test_matrix.py
@@ -836,6 +836,16 @@ def circuit():
         with pytest.raises(ValueError, match=r"wire_order is required"):
             _ = qml.matrix(circuit)
 
+    def test_op_class(self):
+        """Tests that an error is raised when calling qml.matrix without wire_order
+        on an operator class with multiple wires."""
+
+        with pytest.raises(ValueError, match=r"wire_order is required"):
+            _ = qml.matrix(qml.CNOT)(wires=[0, 1])
+
+        # No error should be raised if the operator class has only one wire.
+        _ = qml.matrix(qml.Hadamard)(wires=0)
+
     def test_no_error_cases(self):
         """Test that an error is not raised when calling qml.matrix on an operator, a
         single-wire tape, or a QNode with a device that provides wires."""