diff --git a/crates/accelerate/src/quantum_circuit/circuit_data.rs b/crates/accelerate/src/quantum_circuit/circuit_data.rs
index c162e5237efc..fceb689c0751 100644
--- a/crates/accelerate/src/quantum_circuit/circuit_data.rs
+++ b/crates/accelerate/src/quantum_circuit/circuit_data.rs
@@ -40,6 +40,10 @@ pub struct CircuitData {
 
 #[derive(FromPyObject)]
 pub struct ElementType {
+    // Note that _operation_wrapper is used only to support c_if,
+    // which on the Python-side swaps out the operation that the
+    // wrapper points to.
+    #[pyo3(attribute("_operation_wrapper"))]
     operation: PyObject,
     qubits: Py<PyTuple>,
     clbits: Py<PyTuple>,
diff --git a/qiskit/circuit/quantumcircuitdata.py b/qiskit/circuit/quantumcircuitdata.py
index 7783c5e41815..2042262e630a 100644
--- a/qiskit/circuit/quantumcircuitdata.py
+++ b/qiskit/circuit/quantumcircuitdata.py
@@ -23,6 +23,13 @@
 from .classicalregister import Clbit
 
 
+class _OperationWrapper:
+    operation: Operation
+
+    def __init__(self, op: Operation):
+        self.operation = op
+
+
 class CircuitInstruction:
     """A single instruction in a :class:`.QuantumCircuit`, comprised of the :attr:`operation` and
     various operands.
@@ -58,10 +65,20 @@ class CircuitInstruction:
         of distinct items, with no duplicates.
     """
 
-    __slots__ = ("operation", "qubits", "clbits")
+    __slots__ = ("_operation_wrapper", "qubits", "clbits")
+
+    _operation_wrapper: _OperationWrapper
+
+    @property
+    def operation(self) -> Operation:
+        """The logical operation that this instruction represents an execution of."""
+        return self._operation_wrapper.operation
+
+    @operation.setter
+    def operation(self, op: Operation):
+        """Updates in place the logical operation that this instruction represents an execution of."""
+        self._operation_wrapper.operation = op
 
-    operation: Operation
-    """The logical operation that this instruction represents an execution of."""
     qubits: Tuple[Qubit, ...]
     """A sequence of the qubits that the operation is applied to."""
     clbits: Tuple[Clbit, ...]
@@ -73,14 +90,14 @@ def __init__(
         qubits: Iterable[Qubit] = (),
         clbits: Iterable[Clbit] = (),
     ):
-        self.operation = operation
+        self._operation_wrapper = operation if isinstance(operation, _OperationWrapper) else _OperationWrapper(operation)
         self.qubits = tuple(qubits)
         self.clbits = tuple(clbits)
 
     def copy(self) -> "CircuitInstruction":
         """Return a shallow copy of the :class:`CircuitInstruction`."""
         return self.__class__(
-            operation=self.operation,
+            operation=self._operation_wrapper,
             qubits=self.qubits,
             clbits=self.clbits,
         )