diff --git a/crates/circuit/src/converters.rs b/crates/circuit/src/converters.rs
index 0b853c7ffb08..9619c5ae243d 100644
--- a/crates/circuit/src/converters.rs
+++ b/crates/circuit/src/converters.rs
@@ -40,7 +40,13 @@ impl<'a, 'py> FromPyObject<'a, 'py> for QuantumCircuitData<'py> {
         Ok(QuantumCircuitData {
             data: data_borrowed.borrow().inner.clone(),
             name: ob.getattr(intern!(py, "name"))?.extract()?,
-            metadata: ob.getattr(intern!(py, "metadata")).ok(),
+            metadata: ob.getattr(intern!(py, "metadata")).ok().and_then(|m| {
+                if m.is_none() {
+                    None
+                } else {
+                    m.call_method0(intern!(py, "copy")).ok()
+                }
+            }),
             transpile_layout: ob.getattr(intern!(py, "layout")).ok(),
         })
     }
diff --git a/qiskit/converters/dag_to_circuit.py b/qiskit/converters/dag_to_circuit.py
index 692965fff25c..1fccdedb41a8 100644
--- a/qiskit/converters/dag_to_circuit.py
+++ b/qiskit/converters/dag_to_circuit.py
@@ -68,7 +68,7 @@ def dag_to_circuit(dag, copy_operations=True):
         name=name,
         global_phase=dag.global_phase,
     )
-    circuit.metadata = dag.metadata or {}
+    circuit.metadata = dag.metadata.copy() if dag.metadata else {}
     circuit._data = circuit_data
     circuit._duration = dag._duration
     circuit._unit = dag._unit
diff --git a/test/python/converters/test_circuit_to_dag.py b/test/python/converters/test_circuit_to_dag.py
index 909822f1a3a9..d02c3b8af2c5 100644
--- a/test/python/converters/test_circuit_to_dag.py
+++ b/test/python/converters/test_circuit_to_dag.py
@@ -207,6 +207,19 @@ def test_wire_order_failures(self):
         with self.assertRaisesRegex(ValueError, "does not contain exactly the same"):
             circuit_to_dag(qc, clbit_order=cr[[0, 1, 1]])
 
+    def test_circuit_to_dag_metadata_is_copied(self):
+        """circuit_to_dag should return a DAG with a copy of the metadata, not a reference."""
+        qc = QuantumCircuit(1, metadata={"key": "original"})
+        dag = circuit_to_dag(qc)
+        self.assertIsNot(dag.metadata, qc.metadata)
+        self.assertEqual(dag.metadata, qc.metadata)
+
+    def test_dag_to_circuit_metadata_is_copied(self):
+        """dag_to_circuit should return a circuit with a copy of the metadata, not a reference."""
+        qc = QuantumCircuit(1, metadata={"key": "original"})
+        result = dag_to_circuit(circuit_to_dag(qc))
+        self.assertIsNot(result.metadata, qc.metadata)
+
 
 if __name__ == "__main__":
     unittest.main(verbosity=2)