diff --git a/qiskit/transpiler/passes/utils/gate_direction.py b/qiskit/transpiler/passes/utils/gate_direction.py
index 12cb4ecdcf01..323f19bf7fe9 100644
--- a/qiskit/transpiler/passes/utils/gate_direction.py
+++ b/qiskit/transpiler/passes/utils/gate_direction.py
@@ -166,6 +166,8 @@ def _run_coupling_map(self, dag, wire_map, edges=None):
                 continue
             if len(node.qargs) != 2:
                 continue
+            if dag.has_calibration_for(node):
+                continue
             qargs = (wire_map[node.qargs[0]], wire_map[node.qargs[1]])
             if qargs not in edges and (qargs[1], qargs[0]) not in edges:
                 raise TranspilerError(
@@ -209,6 +211,8 @@ def _run_target(self, dag, wire_map):
                 continue
             if len(node.qargs) != 2:
                 continue
+            if dag.has_calibration_for(node):
+                continue
             qargs = (wire_map[node.qargs[0]], wire_map[node.qargs[1]])
             swapped = (qargs[1], qargs[0])
             if node.name in self._static_replacements:
diff --git a/releasenotes/notes/fix-gate-direction-calibration-c51202358d86e18f.yaml b/releasenotes/notes/fix-gate-direction-calibration-c51202358d86e18f.yaml
new file mode 100644
index 000000000000..140ff5b71028
--- /dev/null
+++ b/releasenotes/notes/fix-gate-direction-calibration-c51202358d86e18f.yaml
@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    The :class:`.GateDirection` transpiler pass will no longer reject gates that have been given
+    explicit calibrations, but do not exist in the generic coupling map or target.
diff --git a/test/python/transpiler/test_gate_direction.py b/test/python/transpiler/test_gate_direction.py
index 3ccb5aa958f4..06c1d814b147 100644
--- a/test/python/transpiler/test_gate_direction.py
+++ b/test/python/transpiler/test_gate_direction.py
@@ -17,8 +17,8 @@
 
 import ddt
 
-from qiskit import ClassicalRegister, QuantumRegister, QuantumCircuit
-from qiskit.circuit import Parameter
+from qiskit import ClassicalRegister, QuantumRegister, QuantumCircuit, pulse
+from qiskit.circuit import Parameter, Gate
 from qiskit.circuit.library import (
     CXGate,
     CZGate,
@@ -439,6 +439,33 @@ def test_target_control_flow(self):
         pass_ = GateDirection(None, target)
         self.assertEqual(pass_(circuit), expected)
 
+    def test_allows_calibrated_gates_coupling_map(self):
+        """Test that the gate direction pass allows a gate that's got a calibration to pass through
+        without error."""
+        cm = CouplingMap([(1, 0)])
+
+        gate = Gate("my_2q_gate", 2, [])
+        circuit = QuantumCircuit(2)
+        circuit.append(gate, (0, 1))
+        circuit.add_calibration(gate, (0, 1), pulse.ScheduleBlock())
+
+        pass_ = GateDirection(cm)
+        self.assertEqual(pass_(circuit), circuit)
+
+    def test_allows_calibrated_gates_target(self):
+        """Test that the gate direction pass allows a gate that's got a calibration to pass through
+        without error."""
+        target = Target(num_qubits=2)
+        target.add_instruction(CXGate(), properties={(0, 1): None})
+
+        gate = Gate("my_2q_gate", 2, [])
+        circuit = QuantumCircuit(2)
+        circuit.append(gate, (0, 1))
+        circuit.add_calibration(gate, (0, 1), pulse.ScheduleBlock())
+
+        pass_ = GateDirection(None, target)
+        self.assertEqual(pass_(circuit), circuit)
+
 
 if __name__ == "__main__":
     unittest.main()