diff --git a/qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py b/qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py
index 503c29f94689..8ed37c400c9c 100644
--- a/qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py
+++ b/qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py
@@ -366,8 +366,8 @@ def _add(self, other, qargs=None):
         return SparsePauliOp(paulis, coeffs, ignore_pauli_phase=True, copy=False)
 
     def _multiply(self, other):
-        if not isinstance(other, Number):
-            raise QiskitError("other is not a number")
+        if not isinstance(other, (Number, ParameterExpression)):
+            raise QiskitError("other is neither a Number nor a Parameter/ParameterExpression")
         if other == 0:
             # Check edge case that we deleted all Paulis
             # In this case we return an identity Pauli with a zero coefficient
diff --git a/releasenotes/notes/support-SparsePauliOp-Parameter-multiplication-245173f0b232f59b.yaml b/releasenotes/notes/support-SparsePauliOp-Parameter-multiplication-245173f0b232f59b.yaml
new file mode 100644
index 000000000000..a140e4aed629
--- /dev/null
+++ b/releasenotes/notes/support-SparsePauliOp-Parameter-multiplication-245173f0b232f59b.yaml
@@ -0,0 +1,15 @@
+features:
+  - |
+    Adds support for multiplication of :class:`.SparsePauliOp` objects
+    with :class:`.Parameter` objects by using the * operator, for example::
+
+      from qiskit.circuit import Parameter
+      from qiskit.quantum_info import SparsePauliOp
+
+      param = Parameter("a")
+      op = SparsePauliOp("X")
+      param * op
+
+fixes:
+  - |
+    Fixes issue `#10185 <https://github.com/Qiskit/qiskit-terra/issues/10185>`.
diff --git a/test/python/quantum_info/operators/symplectic/test_sparse_pauli_op.py b/test/python/quantum_info/operators/symplectic/test_sparse_pauli_op.py
index e9c5d6741bd2..afceedada3e3 100644
--- a/test/python/quantum_info/operators/symplectic/test_sparse_pauli_op.py
+++ b/test/python/quantum_info/operators/symplectic/test_sparse_pauli_op.py
@@ -20,7 +20,7 @@
 from ddt import ddt
 
 from qiskit import QiskitError
-from qiskit.circuit import Parameter, ParameterVector
+from qiskit.circuit import ParameterExpression, Parameter, ParameterVector
 from qiskit.circuit.parametertable import ParameterView
 from qiskit.quantum_info.operators import Operator, Pauli, PauliList, PauliTable, SparsePauliOp
 from qiskit.test import QiskitTestCase
@@ -588,14 +588,28 @@ def test_sub_qargs(self, num_qubits):
         self.assertEqual(value, target)
         np.testing.assert_array_equal(op.paulis.phase, np.zeros(op.size))
 
-    @combine(num_qubits=[1, 2, 3], value=[0, 1, 1j, -3 + 4.4j, np.int64(2)], param=[None, "a"])
+    @combine(
+        num_qubits=[1, 2, 3],
+        value=[
+            0,
+            1,
+            1j,
+            -3 + 4.4j,
+            np.int64(2),
+            Parameter("x"),
+            0 * Parameter("x"),
+            (-2 + 1.7j) * Parameter("x"),
+        ],
+        param=[None, "a"],
+    )
     def test_mul(self, num_qubits, value, param):
         """Test * method for {num_qubits} qubits and value {value}."""
         spp_op = self.random_spp_op(num_qubits, 2**num_qubits, param)
         target = value * spp_op.to_matrix()
         op = value * spp_op
         value_mat = op.to_matrix()
-        if value != 0 and param is not None:
+        has_parameters = isinstance(value, ParameterExpression) or param is not None
+        if value != 0 and has_parameters:
             value_mat = bind_parameters_to_one(value_mat)
             target = bind_parameters_to_one(target)
         if value == 0:
@@ -606,7 +620,7 @@ def test_mul(self, num_qubits, value, param):
         target = spp_op.to_matrix() * value
         op = spp_op * value
         value_mat = op.to_matrix()
-        if value != 0 and param is not None:
+        if value != 0 and has_parameters:
             value_mat = bind_parameters_to_one(value_mat)
             target = bind_parameters_to_one(target)
         if value == 0: