diff --git a/moto/sqs/models.py b/moto/sqs/models.py
index 1d0e86106..6ec47f2ab 100644
--- a/moto/sqs/models.py
+++ b/moto/sqs/models.py
@@ -887,6 +887,17 @@ class SQSBackend(BaseBackend):
             if message.receipt_handle == receipt_handle:
                 if message.visible:
                     raise MessageNotInflight
+
+                visibility_timeout_msec = int(visibility_timeout) * 1000
+                given_visibility_timeout = unix_time_millis() + visibility_timeout_msec
+                if given_visibility_timeout - message.sent_timestamp > 43200 * 1000:
+                    raise InvalidParameterValue(
+                        "Value {0} for parameter VisibilityTimeout is invalid. Reason: Total "
+                        "VisibilityTimeout for the message is beyond the limit [43200 seconds]".format(
+                            visibility_timeout
+                        )
+                    )
+
                 message.change_visibility(visibility_timeout)
                 if message.visible:
                     # If the message is visible again, remove it from pending
diff --git a/tests/test_sqs/test_sqs.py b/tests/test_sqs/test_sqs.py
index 2288cec77..3fe2e025c 100644
--- a/tests/test_sqs/test_sqs.py
+++ b/tests/test_sqs/test_sqs.py
@@ -800,6 +800,41 @@ def test_send_receive_message_with_attributes_with_labels():
     )
 
 
+@mock_sqs
+def test_change_message_visibility_than_permitted():
+    if settings.TEST_SERVER_MODE:
+        raise SkipTest("Cant manipulate time in server mode")
+
+    sqs = boto3.resource("sqs", region_name="us-east-1")
+    conn = boto3.client("sqs", region_name="us-east-1")
+
+    with freeze_time("2015-01-01 12:00:00"):
+        conn.create_queue(QueueName="test-queue-visibility")
+        queue = sqs.Queue("test-queue-visibility")
+        queue.send_message(MessageBody="derp")
+        messages = conn.receive_message(QueueUrl=queue.url)
+        messages.get("Messages").should.have.length_of(1)
+
+        conn.change_message_visibility(
+            QueueUrl=queue.url,
+            ReceiptHandle=messages.get("Messages")[0].get("ReceiptHandle"),
+            VisibilityTimeout=360,
+        )
+
+    with freeze_time("2015-01-01 12:05:00"):
+
+        with pytest.raises(ClientError) as err:
+            conn.change_message_visibility(
+                QueueUrl=queue.url,
+                ReceiptHandle=messages.get("Messages")[0].get("ReceiptHandle"),
+                VisibilityTimeout=43200,
+            )
+
+        ex = err.value
+        ex.operation_name.should.equal("ChangeMessageVisibility")
+        ex.response["Error"]["Code"].should.equal("InvalidParameterValue")
+
+
 @mock_sqs
 def test_send_receive_message_timestamps():
     sqs = boto3.resource("sqs", region_name="us-east-1")
@@ -1869,7 +1904,7 @@ def test_batch_change_message_visibility():
             {
                 "Id": str(uuid.uuid4()),
                 "ReceiptHandle": handle,
-                "VisibilityTimeout": 43200,
+                "VisibilityTimeout": 43000,
             }
             for handle in handles
         ]