diff --git a/qiskit/circuit/commutation_checker.py b/qiskit/circuit/commutation_checker.py
index 5edceab1080f..ad9d4830997a 100644
--- a/qiskit/circuit/commutation_checker.py
+++ b/qiskit/circuit/commutation_checker.py
@@ -65,10 +65,20 @@ def _hashable_parameters(self, params):
         return ("fallback", str(params))
 
     def commute(
-        self, op1: Operation, qargs1: List, cargs1: List, op2: Operation, qargs2: List, cargs2: List
-    ):
+        self,
+        op1: Operation,
+        qargs1: List,
+        cargs1: List,
+        op2: Operation,
+        qargs2: List,
+        cargs2: List,
+        max_num_qubits: int = 3,
+    ) -> bool:
         """
-        Checks if two Operations commute.
+        Checks if two Operations commute. The return value of `True` means that the operations
+        truly commute, and the return value of `False` means that either the operations do not
+        commute or that the commutation check was skipped (for example, when the operations
+        have conditions or have too many qubits).
 
         Args:
             op1: first operation.
@@ -77,10 +87,14 @@ def commute(
             op2: second operation.
             qargs2: second operation's qubits.
             cargs2: second operation's clbits.
+            max_num_qubits: the maximum number of qubits to consider, the check may be skipped if
+                the number of qubits for either operation exceeds this amount.
 
         Returns:
             bool: whether two operations commute.
         """
+        # pylint: disable=too-many-return-statements
+
         # We don't support commutation of conditional gates for now due to bugs in
         # CommutativeCancellation.  See gh-8553.
         if (
@@ -105,6 +119,10 @@ def commute(
         if not (intersection_q or intersection_c):
             return True
 
+        # Skip the check if the number of qubits for either operation is too large
+        if len(qargs1) > max_num_qubits or len(qargs2) > max_num_qubits:
+            return False
+
         # These lines are adapted from commutation_analysis, which is more restrictive than the
         # check from dag_dependency when considering nodes with "_directive".  It would be nice to
         # think which optimizations from dag_dependency can indeed be used.
diff --git a/releasenotes/notes/add-limits-in-commutation-checker-66a1b9e90921621f.yaml b/releasenotes/notes/add-limits-in-commutation-checker-66a1b9e90921621f.yaml
new file mode 100644
index 000000000000..9b8bc6411083
--- /dev/null
+++ b/releasenotes/notes/add-limits-in-commutation-checker-66a1b9e90921621f.yaml
@@ -0,0 +1,14 @@
+---
+features:
+  - |
+    Added a new option ``max_num_qubits`` to :meth:`qiskit.circuit.CommutationChecker.commute`
+    that specifies the maximum number of qubits to consider for the more expensive
+    matrix multiplication-based commutativity check. This avoids trying to
+    internally allocate arrays of size :math:`2^N \times 2^N`. Simpler versions of commutativity
+    check (for instance, two quantum operations commute when they are over disjoint sets of qubits)
+    continue to work without this limit.
+fixes:
+  - |
+    The maximum number of qubits to consider for matrix multiplication-based commutativity check
+    in :class:`~.CommutationChecker` is now limited to 3 by default.
+    Fixed `#10488 <https://github.com/Qiskit/qiskit-terra/issues/10488>`__
diff --git a/test/python/circuit/test_commutation_checker.py b/test/python/circuit/test_commutation_checker.py
index cd1b08d0ceb9..bfb41e649a12 100644
--- a/test/python/circuit/test_commutation_checker.py
+++ b/test/python/circuit/test_commutation_checker.py
@@ -25,6 +25,7 @@
     XGate,
     CXGate,
     CCXGate,
+    MCXGate,
     RZGate,
     Measure,
     Barrier,
@@ -362,6 +363,20 @@ def test_c7x_gate(self):
         res = CommutationChecker().commute(XGate(), qargs[:1], [], XGate().control(7), qargs, [])
         self.assertFalse(res)
 
+    def test_wide_gates_over_nondisjoint_qubits(self):
+        """Test that checking wide gates does not lead to memory problems."""
+        res = CommutationChecker().commute(MCXGate(29), list(range(30)), [], XGate(), [0], [])
+        self.assertFalse(res)
+        res = CommutationChecker().commute(XGate(), [0], [], MCXGate(29), list(range(30)), [])
+        self.assertFalse(res)
+
+    def test_wide_gates_over_disjoint_qubits(self):
+        """Test that wide gates still commute when they are over disjoint sets of qubits."""
+        res = CommutationChecker().commute(MCXGate(29), list(range(30)), [], XGate(), [30], [])
+        self.assertTrue(res)
+        res = CommutationChecker().commute(XGate(), [30], [], MCXGate(29), list(range(30)), [])
+        self.assertTrue(res)
+
 
 if __name__ == "__main__":
     unittest.main()