diff --git a/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py b/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py
index 129fce9469db..f77870047c9d 100644
--- a/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py
+++ b/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py
@@ -57,6 +57,7 @@ class MergeAdjacentBarriers(TransformationPass):
 
     def run(self, dag):
         """Run the MergeAdjacentBarriers pass on `dag`."""
+        indices = {qubit: index for index, qubit in enumerate(dag.qubits)}
 
         # sorted to so that they are in the order they appear in the DAG
         # so ancestors/descendants makes sense
@@ -77,7 +78,9 @@ def run(self, dag):
                 if node in node_to_barrier_qubits:
                     qubits = node_to_barrier_qubits[node]
                     # qubits are stored as a set, need to convert to a list
-                    new_dag.apply_operation_back(Barrier(len(qubits)), qargs=list(qubits))
+                    new_dag.apply_operation_back(
+                        Barrier(len(qubits)), qargs=sorted(qubits, key=indices.get)
+                    )
             else:
                 # copy the condition over too
                 new_dag.apply_operation_back(node.op, qargs=node.qargs, cargs=node.cargs)
diff --git a/releasenotes/notes/deterministic-barrier-before-final-measurements-04e817d995794067.yaml b/releasenotes/notes/deterministic-barrier-before-final-measurements-04e817d995794067.yaml
new file mode 100644
index 000000000000..eda25b1e4763
--- /dev/null
+++ b/releasenotes/notes/deterministic-barrier-before-final-measurements-04e817d995794067.yaml
@@ -0,0 +1,9 @@
+---
+fixes:
+  - |
+    The :class:`.BarrierBeforeFinalMeasurements` and :class:`.MergeAdjacentBarriers` transpiler
+    passes previously had a non-deterministic order of their emitted :class:`.Barrier` instructions.
+    This did not change the semantics of circuits but could, in limited cases where there were
+    non-full-width barriers, cause later stochastic transpiler passes to see a different topological
+    ordering of the circuit and consequently have different outputs for fixed seeds.  The passes
+    have been made deterministic to avoid this.
diff --git a/test/python/transpiler/test_adjacent_barriers.py b/test/python/transpiler/test_adjacent_barriers.py
index c6cb13372ca7..e979a6a25bef 100644
--- a/test/python/transpiler/test_adjacent_barriers.py
+++ b/test/python/transpiler/test_adjacent_barriers.py
@@ -12,6 +12,7 @@
 
 """Test the MergeAdjacentBarriers pass"""
 
+import random
 import unittest
 from qiskit.transpiler.passes import MergeAdjacentBarriers
 from qiskit.converters import circuit_to_dag
@@ -271,6 +272,28 @@ def test_barriers_with_blocking_obstacle_twoQ(self):
 
         self.assertEqual(result, circuit_to_dag(expected))
 
+    def test_output_deterministic(self):
+        """Test that the output barriers have a deterministic ordering (independent of
+        PYTHONHASHSEED).  This is important to guarantee that any subsequent topological iterations
+        through the circuit are also deterministic; it's in general not possible for all transpiler
+        passes to produce identical outputs across all valid topological orderings, especially if
+        those passes have some stochastic element."""
+        order = list(range(20))
+        random.Random(2023_02_10).shuffle(order)
+        circuit = QuantumCircuit(20)
+        circuit.barrier([5, 2, 3])
+        circuit.barrier([7, 11, 14, 2, 4])
+        circuit.barrier(order)
+
+        # All the barriers should get merged together.
+        expected = QuantumCircuit(20)
+        expected.barrier(range(20))
+
+        output = MergeAdjacentBarriers()(circuit)
+        self.assertEqual(expected, output)
+        # This assertion is that the ordering of the arguments in the barrier is fixed.
+        self.assertEqual(list(output.data[0].qubits), list(output.qubits))
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/test/python/transpiler/test_barrier_before_final_measurements.py b/test/python/transpiler/test_barrier_before_final_measurements.py
index 6edc7b3fa959..4b879e0e290a 100644
--- a/test/python/transpiler/test_barrier_before_final_measurements.py
+++ b/test/python/transpiler/test_barrier_before_final_measurements.py
@@ -12,6 +12,7 @@
 
 """Test the BarrierBeforeFinalMeasurements pass"""
 
+import random
 import unittest
 from qiskit.transpiler.passes import BarrierBeforeFinalMeasurements
 from qiskit.converters import circuit_to_dag
@@ -392,6 +393,29 @@ def test_conditioned_on_single_bit(self):
         pass_ = BarrierBeforeFinalMeasurements()
         self.assertEqual(expected, pass_(circuit))
 
+    def test_output_deterministic(self):
+        """Test that the output barriers have a deterministic ordering (independent of
+        PYTHONHASHSEED).  This is important to guarantee that any subsequent topological iterations
+        through the circuit are also deterministic; it's in general not possible for all transpiler
+        passes to produce identical outputs across all valid topological orderings, especially if
+        those passes have some stochastic element."""
+        measure_order = list(range(20))
+        random.Random(2023_02_10).shuffle(measure_order)
+        circuit = QuantumCircuit(20, 20)
+        circuit.barrier([5, 2, 3])
+        circuit.barrier([7, 11, 14, 2, 4])
+        circuit.measure(measure_order, measure_order)
+
+        # All the barriers should get merged together.
+        expected = QuantumCircuit(20, 20)
+        expected.barrier(range(20))
+        expected.measure(measure_order, measure_order)
+
+        output = BarrierBeforeFinalMeasurements()(circuit)
+        self.assertEqual(expected, output)
+        # This assertion is that the ordering of the arguments in the barrier is fixed.
+        self.assertEqual(list(output.data[0].qubits), list(output.qubits))
+
 
 if __name__ == "__main__":
     unittest.main()