diff --git a/pennylane/measurements/mid_measure.py b/pennylane/measurements/mid_measure.py
index 971eb8bcb87..a941f2b9e59 100644
--- a/pennylane/measurements/mid_measure.py
+++ b/pennylane/measurements/mid_measure.py
@@ -222,7 +222,7 @@ def func(x):
         raise NotImplementedError(
             "Capture cannot currently handle classical output from mid circuit measurements."
         )
-    return MeasurementValue([mp], processing_fn=lambda v: v)
+    return mp.mv
 
 
 T = TypeVar("T")
@@ -261,6 +261,14 @@ def __init__(
         super().__init__(wires=Wires(wires), id=id)
         self.reset = reset
         self.postselect = postselect
+        self.mv = MeasurementValue([self], processing_fn=lambda v: v)
+
+    @property
+    def wires(self):
+        # Overriden wires property as MeasurementProcess.wires uses mv.wires when mv is not None,
+        # and MeasurementValue.wires uses the wires of the mid-circuit measurements, which would
+        # lead to infinite recursion.
+        return self._wires
 
     # pylint: disable=arguments-renamed, arguments-differ
     @classmethod
diff --git a/pennylane/transforms/dynamic_one_shot.py b/pennylane/transforms/dynamic_one_shot.py
index bbd83c1bada..40c91b1679f 100644
--- a/pennylane/transforms/dynamic_one_shot.py
+++ b/pennylane/transforms/dynamic_one_shot.py
@@ -27,7 +27,6 @@
 from pennylane.measurements import (
     CountsMP,
     ExpectationMP,
-    MeasurementValue,
     MidMeasureMP,
     ProbabilityMP,
     SampleMP,
@@ -210,12 +209,7 @@ def init_auxiliary_tape(circuit: qml.tape.QuantumScript):
                 new_measurements.append(m)
     for op in circuit.operations:
         if isinstance(op, MidMeasureMP):
-            mv = (
-                op.mcm_tracer
-                if "MidCircuitMeasure" in str(type(op))
-                else MeasurementValue([op], lambda res: res)
-            )
-            new_measurements.append(qml.sample(op=mv))
+            new_measurements.append(qml.sample(op=op.mv))
     return qml.tape.QuantumScript(
         circuit.operations,
         new_measurements,
@@ -326,7 +320,7 @@ def gather_mcm_qjit(measurement, samples, is_valid):  # pragma: no cover
     """
     found, meas = False, None
     for k, meas in samples.items():
-        if measurement.mv is k.mcm_tracer:
+        if measurement.mv is k.mv:
             found = True
             break
     if not found: