diff --git a/moto/ssm/models.py b/moto/ssm/models.py
index 74f60e58a..fe6c64ee8 100644
--- a/moto/ssm/models.py
+++ b/moto/ssm/models.py
@@ -1217,7 +1217,12 @@ class SimpleSystemManagerBackend(BaseBackend):
                     )
                     if len(result) > 0:
                         return result[-1]
-
+                    elif len(parameters) > 0:
+                        raise ParameterVersionNotFound(
+                            "Systems Manager could not find version %s of %s. "
+                            "Verify the version and try again."
+                            % (version_or_label, name_prefix)
+                        )
                 result = list(
                     filter(lambda x: version_or_label in x.labels, parameters)
                 )
diff --git a/tests/test_ssm/test_ssm_boto3.py b/tests/test_ssm/test_ssm_boto3.py
index 3301ed32c..ddf033cfc 100644
--- a/tests/test_ssm/test_ssm_boto3.py
+++ b/tests/test_ssm/test_ssm_boto3.py
@@ -465,8 +465,15 @@ def test_get_parameter_with_version_and_labels():
 
     with pytest.raises(ClientError) as ex:
         client.get_parameter(Name="test-2:2", WithDecryption=False)
+    ex.value.response["Error"]["Code"].should.equal("ParameterVersionNotFound")
+    ex.value.response["Error"]["Message"].should.equal(
+        "Systems Manager could not find version 2 of test-2. Verify the version and try again."
+    )
+
+    with pytest.raises(ClientError) as ex:
+        client.get_parameter(Name="test-3:2", WithDecryption=False)
     ex.value.response["Error"]["Code"].should.equal("ParameterNotFound")
-    ex.value.response["Error"]["Message"].should.equal("Parameter test-2:2 not found.")
+    ex.value.response["Error"]["Message"].should.equal("Parameter test-3:2 not found.")
 
 
 @mock_ssm