diff --git a/qiskit/quantum_info/operators/operator.py b/qiskit/quantum_info/operators/operator.py
index dd5b340d8240..413731e6fe9f 100644
--- a/qiskit/quantum_info/operators/operator.py
+++ b/qiskit/quantum_info/operators/operator.py
@@ -21,6 +21,7 @@
 import numpy as np
 
 from qiskit.circuit.quantumcircuit import QuantumCircuit
+from qiskit.circuit.instruction import Instruction
 from qiskit.circuit.operation import Operation
 from qiskit.circuit.library.standard_gates import IGate, XGate, YGate, ZGate, HGate, SGate, TGate
 from qiskit.exceptions import QiskitError
@@ -514,11 +515,16 @@ def _init_instruction(cls, instruction):
     @classmethod
     def _instruction_to_matrix(cls, obj):
         """Return Operator for instruction if defined or None otherwise."""
-        # Note: to_matrix() is not a required method for Operations, thus we raise
-        # an error for opaque instructions without a matrix representation.
-        # On the other hand, we do use to_matrix() when it's available.
-        if not isinstance(obj, Operation) and not hasattr(obj, "to_matrix"):
-            raise QiskitError("Input is not an Operation and does not have 'to_matrix()' method.")
+        # Note: to_matrix() is not a required method for Operations, so for now
+        # we do not allow constructing matrices for general Operations.
+        # However, for backward compatibility we need to support constructing matrices
+        # for Cliffords, which happen to have a to_matrix() method.
+
+        # pylint: disable=cyclic-import
+        from qiskit.quantum_info import Clifford
+
+        if not isinstance(obj, (Instruction, Clifford)):
+            raise QiskitError("Input is neither an Instruction nor Clifford.")
         mat = None
         if hasattr(obj, "to_matrix"):
             # If instruction is a gate first we see if it has a