diff --git a/qiskit/quantum_info/states/statevector.py b/qiskit/quantum_info/states/statevector.py
index 3fc58ee4f9a6..f8aaf4c8432c 100644
--- a/qiskit/quantum_info/states/statevector.py
+++ b/qiskit/quantum_info/states/statevector.py
@@ -1027,7 +1027,8 @@ def _evolve_instruction(statevec, obj, qargs=None):
             )
 
         if obj.definition.global_phase:
-            statevec._data *= np.exp(1j * float(obj.definition.global_phase))
+            # We do not apply this in-place, just in-case we have a shallow copy of _data.
+            statevec._data = statevec._data * np.exp(1j * float(obj.definition.global_phase))
         qubits = {qubit: i for i, qubit in enumerate(obj.definition.qubits)}
         for instruction in obj.definition:
             if instruction.clbits:
diff --git a/releasenotes/notes/fix-statevector-evolve-inplace-modification-be2f31976d5a2e1d.yaml b/releasenotes/notes/fix-statevector-evolve-inplace-modification-be2f31976d5a2e1d.yaml
new file mode 100644
index 000000000000..2672766a0d1e
--- /dev/null
+++ b/releasenotes/notes/fix-statevector-evolve-inplace-modification-be2f31976d5a2e1d.yaml
@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixed :meth:`.Statevector.evolve` modifying the input statevector in-place when the
+    instruction has a global phase.
+    See `#15750 <https://github.com/Qiskit/qiskit/issues/15750>`__.
diff --git a/test/python/quantum_info/states/test_statevector.py b/test/python/quantum_info/states/test_statevector.py
index a72a327dd994..b4c8df7691f8 100644
--- a/test/python/quantum_info/states/test_statevector.py
+++ b/test/python/quantum_info/states/test_statevector.py
@@ -23,7 +23,7 @@
 from qiskit import QiskitError
 from qiskit import QuantumRegister, QuantumCircuit
 from qiskit import transpile
-from qiskit.circuit.library import HGate, QFTGate, GlobalPhaseGate
+from qiskit.circuit.library import HGate, QFTGate, GlobalPhaseGate, DiagonalGate, CXGate, XGate
 from qiskit.providers.basic_provider import BasicSimulator
 from qiskit.utils import optionals
 from qiskit.quantum_info.random import random_unitary, random_statevector, random_pauli
@@ -336,6 +336,115 @@ def test_evolve(self):
             evolved = Statevector(vec).evolve(op)
             self.assertEqual(target, evolved)
 
+    def test_evolve_no_modification_with_xgate(self):
+        """Test evolve by XGate doesn't modify original vector"""
+
+        # |00> is sensitive to IX
+        original_vec = Statevector([1.0, 0.0, 0.0, 0.0])
+
+        # Copy so we can compare to original_vec
+        new_vec = original_vec.copy()
+        evolved_vec = new_vec.evolve(XGate(), [0])
+
+        # Check that the evolved state is different to the original state. If they aren't, then
+        # either our initial state is an eigenstate of the operator or evolve() with the given
+        # operator is broken.
+        self.assertNotEqual(
+            evolved_vec,
+            original_vec,
+            "The evolved state is unchanged. Either the state is an eigenvector or evolve() is broken.",
+        )
+        self.assertEqual(original_vec, new_vec, "Evolving by XGate modified original Statevector")
+
+    def test_evolve_no_modification_with_cxgate(self):
+        """Test evolve by CXGate doesn't modify original vector"""
+
+        # |01> is sensitive to CX
+        original_vec = Statevector([0.0, 1.0, 0.0, 0.0])
+
+        # Copy so we can compare to original_vec
+        new_vec = original_vec.copy()
+        evolved_vec = new_vec.evolve(CXGate(), [0, 1])
+
+        # Check that the evolved state is different to the original state. If they aren't, then
+        # either our initial state is an eigenstate of the operator or evolve() with the given
+        # operator is broken.
+        self.assertNotEqual(
+            evolved_vec,
+            original_vec,
+            "The evolved state is unchanged. Either the state is an eigenvector or evolve() is broken.",
+        )
+        self.assertEqual(original_vec, new_vec, "Evolving by CXGate modified original Statevector")
+
+    def test_evolve_no_modification_with_diagonalgate(self):
+        """Test evolve by DiagonalGate doesn't modify original vector"""
+
+        # All superposition is sensitive to the given DiagonalGate
+        original_vec = Statevector(np.ones(4) / np.sqrt(4))
+
+        # Copy so we can compare to original_vec
+        new_vec = original_vec.copy()
+        evolved_vec = new_vec.evolve(DiagonalGate([1.0, -1.0, -1.0, 1.0]), [0, 1])
+
+        # Check that the evolved state is different to the original state. If they aren't, then
+        # either our initial state is an eigenstate of the operator or evolve() with the given
+        # operator is broken.
+        self.assertNotEqual(
+            evolved_vec,
+            original_vec,
+            "The evolved state is unchanged. Either the state is an eigenvector or evolve() is broken.",
+        )
+        self.assertEqual(
+            original_vec, new_vec, "Evolving by DiagonalGate modified original Statevector"
+        )
+
+    def test_evolve_no_modification_with_operator(self):
+        """Test evolve by Operator doesn't modify original vector"""
+
+        # |0> is sensitive to X
+        original_vec = Statevector([1.0, 0.0, 0.0, 0.0])
+        # Copy so we can compare to original_vec
+        new_vec = original_vec.copy()
+        evolved_vec = new_vec.evolve(Operator(XGate()), [0])
+
+        # Check that the evolved state is different to the original state. If they aren't, then
+        # either our initial state is an eigenstate of the operator or evolve() with the given
+        # operator is broken.
+        self.assertNotEqual(
+            evolved_vec,
+            original_vec,
+            "The evolved state is unchanged. Either the state is an eigenvector or evolve() is broken.",
+        )
+        self.assertEqual(
+            original_vec, new_vec, "Evolving by Operator modified original Statevector"
+        )
+
+    def test_evolve_no_modification_with_quantumcircuit(self):
+        """Test by QuantumCircuit method doesn't modify original vector"""
+
+        # |00> is sensitive to a Bell-state preparation circuit
+        original_vec = Statevector([1.0, 0.0, 0.0, 0.0])
+
+        # Copy so we can compare to original_vec
+        new_vec = original_vec.copy()
+        circ = QuantumCircuit(2)
+        circ.h(0)
+        circ.cx(0, 1)
+        evolved_vec = new_vec.evolve(circ, [0, 1])
+
+        # Check that the evolved state is different to the original state. If they aren't, then
+        # either our initial state is an eigenstate of the operator or evolve() with the given
+        # operator is broken.
+
+        self.assertNotEqual(
+            evolved_vec,
+            original_vec,
+            "The evolved state is unchanged. Either the state is an eigenvector or evolve() is broken.",
+        )
+        self.assertEqual(
+            original_vec, new_vec, "Evolving by QuantumCircuit modified original Statevector"
+        )
+
     def test_evolve_operator_overload_dimensions(self):
         """Test that the @ operator returns a Statevector of correct dimension, type and value."""
         op = random_unitary(4)  # 4x4 unitary