diff --git a/qiskit/circuit/quantumcircuit.py b/qiskit/circuit/quantumcircuit.py
index 16d5810b773c..6918a0a01805 100644
--- a/qiskit/circuit/quantumcircuit.py
+++ b/qiskit/circuit/quantumcircuit.py
@@ -334,8 +334,12 @@ def extend(self, rhs):
             if element not in self.cregs:
                 self.cregs.append(element)
 
+        # Copy the circuit data if rhs and self are the same, otherwise the data of rhs is
+        # appended to both self and rhs resulting in an infinite loop
+        data = rhs.data.copy() if rhs is self else rhs.data
+
         # Add new gates
-        for instruction_context in rhs.data:
+        for instruction_context in data:
             self._append(*instruction_context)
         return self
 
diff --git a/releasenotes/notes/copy-rhs-on-extending-qc-9e65804b6b0ab4da.yaml b/releasenotes/notes/copy-rhs-on-extending-qc-9e65804b6b0ab4da.yaml
new file mode 100644
index 000000000000..9a822a74c2e4
--- /dev/null
+++ b/releasenotes/notes/copy-rhs-on-extending-qc-9e65804b6b0ab4da.yaml
@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    When extending a `QuantumCircuit` instance (extendee) with another circuit (extension),
+    the circuit is taken via reference. If a circuit is extended with itself that
+    leads to an infinite loop as extendee and extension are the same.
+    This bug is resolved by copying the extension if it is the same object as
+    the extendee.
\ No newline at end of file
diff --git a/test/python/circuit/test_circuit_operations.py b/test/python/circuit/test_circuit_operations.py
index 4afc9d59ddf2..4f00778aa492 100644
--- a/test/python/circuit/test_circuit_operations.py
+++ b/test/python/circuit/test_circuit_operations.py
@@ -25,6 +25,22 @@
 class TestCircuitOperations(QiskitTestCase):
     """QuantumCircuit Operations tests."""
 
+    def test_adding_self(self):
+        """Test that qc += qc finishes, which can be prone to infinite while-loops.
+
+        This can occur e.g. when a user tries
+        >>> other_qc = qc
+        >>> other_qc += qc  # or qc2.extend(qc)
+        """
+        qc = QuantumCircuit(1)
+        qc.x(0)  # must contain at least one operation to end up in a infinite while-loop
+
+        # attempt addition, times out if qc is added via reference
+        qc += qc
+
+        # finally, qc should contain two X gates
+        self.assertEqual(['x', 'x'], [x[0].name for x in qc.data])
+
     def test_combine_circuit_common(self):
         """Test combining two circuits with same registers.
         """