diff --git a/qiskit/circuit/quantumcircuit.py b/qiskit/circuit/quantumcircuit.py
index 5dfea905bdc..8727d78b810 100644
--- a/qiskit/circuit/quantumcircuit.py
+++ b/qiskit/circuit/quantumcircuit.py
@@ -5025,7 +5025,9 @@ def _qasm2_define_custom_operation(operation, existing_gate_names, gates_to_defi
 
     Returns a potentially new :class:`.Instruction`, which should be used for the
     :meth:`~.Instruction.qasm` call (it may have been renamed)."""
-    from qiskit.circuit import library as lib  # pylint: disable=cyclic-import
+    # pylint: disable=cyclic-import
+    from qiskit.circuit import library as lib
+    from qiskit.qasm2 import QASM2ExportError
 
     if operation.name in existing_gate_names:
         return operation
@@ -5086,6 +5088,17 @@ def _qasm2_define_custom_operation(operation, existing_gate_names, gates_to_defi
         )
     else:
         parameters_qasm = ""
+
+    if operation.num_qubits == 0:
+        raise QASM2ExportError(
+            f"OpenQASM 2 cannot represent '{operation.name}, which acts on zero qubits."
+        )
+    if operation.num_clbits != 0:
+        raise QASM2ExportError(
+            f"OpenQASM 2 cannot represent '{operation.name}', which acts on {operation.num_clbits}"
+            " classical bits."
+        )
+
     qubits_qasm = ",".join(f"q{i}" for i in range(parameterized_operation.num_qubits))
     parameterized_definition = getattr(parameterized_operation, "definition", None)
     if parameterized_definition is None:
diff --git a/releasenotes/notes/qasm_invalid_custom_instruction-7738db7ba1a1a5cf.yaml b/releasenotes/notes/qasm_invalid_custom_instruction-7738db7ba1a1a5cf.yaml
new file mode 100644
index 00000000000..545032c17a1
--- /dev/null
+++ b/releasenotes/notes/qasm_invalid_custom_instruction-7738db7ba1a1a5cf.yaml
@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    Qiskit can represent custom instructions that act on zero qubits, or on a non-zero number of
+    classical bits.  These cannot be exported to OpenQASM 2, but previously :meth:`.QuantumCircuit.qasm`
+    would try, and output invalid OpenQASM 2.  Instead, a :exc:`.QASM2ExportError` will now correctly
+    be raised.  See `#7351 <https://github.com/Qiskit/qiskit-terra/issues/7351>`__ and
+    `#10435 <https://github.com/Qiskit/qiskit-terra/issues/10435>`__.
diff --git a/test/python/circuit/test_circuit_qasm.py b/test/python/circuit/test_circuit_qasm.py
index 32f12e2c89e..83e1d7999a4 100644
--- a/test/python/circuit/test_circuit_qasm.py
+++ b/test/python/circuit/test_circuit_qasm.py
@@ -657,6 +657,30 @@ def test_circuit_raises_on_single_bit_condition(self):
         with self.assertRaisesRegex(QasmError, "OpenQASM 2 can only condition on registers"):
             qc.qasm()
 
+    def test_circuit_raises_invalid_custom_gate_no_qubits(self):
+        """OpenQASM 2 exporter of custom gates with no qubits.
+        See: https://github.com/Qiskit/qiskit-terra/issues/10435"""
+        legit_circuit = QuantumCircuit(5, name="legit_circuit")
+        empty_circuit = QuantumCircuit(name="empty_circuit")
+        legit_circuit.append(empty_circuit)
+
+        with self.assertRaisesRegex(QasmError, "acts on zero qubits"):
+            legit_circuit.qasm()
+
+    def test_circuit_raises_invalid_custom_gate_clbits(self):
+        """OpenQASM 2 exporter of custom instruction.
+        See: https://github.com/Qiskit/qiskit-terra/issues/7351"""
+        instruction = QuantumCircuit(2, 2, name="inst")
+        instruction.cx(0, 1)
+        instruction.measure([0, 1], [0, 1])
+        custom_instruction = instruction.to_instruction()
+
+        qc = QuantumCircuit(2, 2)
+        qc.append(custom_instruction, [0, 1], [0, 1])
+
+        with self.assertRaisesRegex(QasmError, "acts on 2 classical bits"):
+            qc.qasm()
+
     def test_circuit_qasm_with_permutations(self):
         """Test circuit qasm() method with Permutation gates."""