diff --git a/qiskit/circuit/duration.py b/qiskit/circuit/duration.py
index 88ce7af968e..6acb230baad 100644
--- a/qiskit/circuit/duration.py
+++ b/qiskit/circuit/duration.py
@@ -78,8 +78,15 @@ def convert_durations_to_dt(qc: QuantumCircuit, dt_in_sec: float, inplace=True):
         operation.duration = duration_in_dt(duration, dt_in_sec)
         operation.unit = "dt"
 
-    if circ.duration is not None:
-        circ.duration = duration_in_dt(circ.duration, dt_in_sec)
+    if circ.duration is not None and circ.unit != "dt":
+        if not circ.unit.endswith("s"):
+            raise CircuitError(f"Invalid time unit: '{circ.unit}'")
+
+        duration = circ.duration
+        if circ.unit != "s":
+            duration = apply_prefix(duration, circ.unit)
+
+        circ.duration = duration_in_dt(duration, dt_in_sec)
         circ.unit = "dt"
 
     if not inplace:
diff --git a/releasenotes/notes/fix-scheduling-units-59477912b47d3dc1.yaml b/releasenotes/notes/fix-scheduling-units-59477912b47d3dc1.yaml
new file mode 100644
index 00000000000..72f4b46fc73
--- /dev/null
+++ b/releasenotes/notes/fix-scheduling-units-59477912b47d3dc1.yaml
@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    A bug has been fixed in :func:`.convert_durations_to_dt` where the function would blindly apply
+    a conversion from seconds to ``dt`` on circuit durations, independently of the original units of the attribute.
+    This could lead to wrong orders of magnitude in the reported circuit durations.
diff --git a/test/python/circuit/test_scheduled_circuit.py b/test/python/circuit/test_scheduled_circuit.py
index 35441076290..ec4bc72ffd0 100644
--- a/test/python/circuit/test_scheduled_circuit.py
+++ b/test/python/circuit/test_scheduled_circuit.py
@@ -18,8 +18,10 @@
 from qiskit import QuantumCircuit, QiskitError
 from qiskit import transpile, assemble
 from qiskit.circuit import Parameter
-from qiskit.providers.fake_provider import Fake27QPulseV1
+from qiskit.circuit.duration import convert_durations_to_dt
+from qiskit.providers.fake_provider import Fake27QPulseV1, GenericBackendV2
 from qiskit.providers.basic_provider import BasicSimulator
+from qiskit.scheduler import ScheduleConfig
 from qiskit.transpiler.exceptions import TranspilerError
 from qiskit.transpiler.instruction_durations import InstructionDurations
 from test import QiskitTestCase  # pylint: disable=wrong-import-order
@@ -300,6 +302,48 @@ def test_per_qubit_durations(self):
         self.assertEqual(sc.qubit_start_time(*q), 300)
         self.assertEqual(sc.qubit_stop_time(*q), 2400)
 
+    def test_convert_duration_to_dt(self):
+        """Test that circuit duration unit conversion is applied only when necessary.
+        Tests fix for bug reported in PR #11782."""
+
+        backend = GenericBackendV2(num_qubits=3, calibrate_instructions=True, seed=10)
+        schedule_config = ScheduleConfig(
+            inst_map=backend.target.instruction_schedule_map(),
+            meas_map=backend.meas_map,
+            dt=backend.dt,
+        )
+
+        circ = QuantumCircuit(2)
+        circ.cx(0, 1)
+        circ.measure_all()
+
+        circuit_dt = transpile(circ, backend, scheduling_method="asap")
+        # reference duration and unit in dt
+        ref_duration = circuit_dt.duration
+        ref_unit = circuit_dt.unit
+
+        circuit_s = circuit_dt.copy()
+        circuit_s.duration *= backend.dt
+        circuit_s.unit = "s"
+
+        circuit_ms = circuit_s.copy()
+        circuit_ms.duration *= 1000
+        circuit_ms.unit = "ms"
+
+        for circuit in [circuit_dt, circuit_s, circuit_ms]:
+            with self.subTest(circuit=circuit):
+                converted_circ = convert_durations_to_dt(
+                    circuit, dt_in_sec=schedule_config.dt, inplace=False
+                )
+                self.assertEqual(
+                    converted_circ.duration,
+                    ref_duration,
+                )
+                self.assertEqual(
+                    converted_circ.unit,
+                    ref_unit,
+                )
+
     def test_change_dt_in_transpile(self):
         qc = QuantumCircuit(1, 1)
         qc.x(0)