diff --git a/qiskit/circuit/library/generalized_gates/permutation.py b/qiskit/circuit/library/generalized_gates/permutation.py
index aa27a6b20fdc..0dd8e0f9df7f 100644
--- a/qiskit/circuit/library/generalized_gates/permutation.py
+++ b/qiskit/circuit/library/generalized_gates/permutation.py
@@ -186,7 +186,7 @@ def inverse(self, annotated: bool = False) -> PermutationGate:
 
         return PermutationGate(pattern=_inverse_pattern(self.pattern))
 
-    def _qasm2_decomposition(self):
+    def _qasm_decomposition(self):
         # pylint: disable=cyclic-import
         from qiskit.synthesis.permutation import synth_permutation_basic
 
diff --git a/qiskit/circuit/library/generalized_gates/unitary.py b/qiskit/circuit/library/generalized_gates/unitary.py
index 40271ed4f594..a1550d1a7acb 100644
--- a/qiskit/circuit/library/generalized_gates/unitary.py
+++ b/qiskit/circuit/library/generalized_gates/unitary.py
@@ -202,7 +202,7 @@ def control(
             )
         return gate
 
-    def _qasm2_decomposition(self):
+    def _qasm_decomposition(self):
         """Return an unparameterized version of ourselves, so the OQ2 exporter doesn't choke on the
         non-standard things in our `params` field."""
         out = self.definition.to_gate()
diff --git a/qiskit/qasm2/export.py b/qiskit/qasm2/export.py
index 7c655dfd432b..fbe9b533ea9a 100644
--- a/qiskit/qasm2/export.py
+++ b/qiskit/qasm2/export.py
@@ -314,8 +314,8 @@ def _define_custom_operation(operation, gates_to_define):
     # definition, but still continue to return the given object as the call-site object.
     if operation.base_class in known_good_parameterized:
         parameterized_operation = type(operation)(*_FIXED_PARAMETERS[: len(operation.params)])
-    elif hasattr(operation, "_qasm2_decomposition"):
-        new_op = operation._qasm2_decomposition()
+    elif hasattr(operation, "_qasm_decomposition"):
+        new_op = operation._qasm_decomposition()
         parameterized_operation = operation = new_op.copy(name=_escape_name(new_op.name, "gate_"))
     else:
         parameterized_operation = operation
diff --git a/qiskit/qasm3/exporter.py b/qiskit/qasm3/exporter.py
index 8997770c14e7..b08b2a9719ef 100644
--- a/qiskit/qasm3/exporter.py
+++ b/qiskit/qasm3/exporter.py
@@ -1180,13 +1180,16 @@ def build_gate_call(self, instruction: CircuitInstruction):
 
         This will also push the gate into the symbol table (if required), including recursively
         defining the gate blocks."""
-        ident = self.symbols.get_gate(instruction.operation)
+        operation = instruction.operation
+        if hasattr(operation, "_qasm_decomposition"):
+            operation = operation._qasm_decomposition()
+        ident = self.symbols.get_gate(operation)
         if ident is None:
-            ident = self.define_gate(instruction.operation)
+            ident = self.define_gate(operation)
         qubits = [self._lookup_bit(qubit) for qubit in instruction.qubits]
         parameters = [
             ast.StringifyAndPray(self._rebind_scoped_parameters(param))
-            for param in instruction.operation.params
+            for param in operation.params
         ]
         if not self.disable_constants:
             for parameter in parameters:
diff --git a/releasenotes/notes/fix-qasm-3-unitary-2da190be6ba25bbd.yaml b/releasenotes/notes/fix-qasm-3-unitary-2da190be6ba25bbd.yaml
new file mode 100644
index 000000000000..3cd59ff5e427
--- /dev/null
+++ b/releasenotes/notes/fix-qasm-3-unitary-2da190be6ba25bbd.yaml
@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fix a bug in :class:`.qasm3.Exporter` that caused the exporter to crash when
+    handling a unitary gate due to incorrect processing of its ``params`` field.
diff --git a/test/python/qasm3/test_export.py b/test/python/qasm3/test_export.py
index acae1d7d3cd7..1b9c24ca5410 100644
--- a/test/python/qasm3/test_export.py
+++ b/test/python/qasm3/test_export.py
@@ -2665,6 +2665,23 @@ def test_switch_v1_expr_target(self):
         test = dumps(qc, experimental=ExperimentalFeatures.SWITCH_CASE_V1)
         self.assertEqual(test, expected)
 
+    def test_circuit_with_unitary(self):
+        """Test that circuits with `unitary` gate are correctly handled"""
+        matrix = [[0, 1], [1, 0]]
+        qc = QuantumCircuit(1)
+        qc.unitary(matrix, [0])
+        expected = """\
+OPENQASM 3.0;
+include "stdgates.inc";
+gate unitary _gate_q_0 {
+  U(pi, -pi, 0) _gate_q_0;
+}
+qubit[1] q;
+unitary q[0];
+"""
+        test = dumps(qc)
+        self.assertEqual(test, expected)
+
 
 @ddt
 class TestQASM3ExporterFailurePaths(QiskitTestCase):