diff --git a/setup.py b/setup.py
index f4d7c2f7b..f1ddaf2ac 100644
--- a/setup.py
+++ b/setup.py
@@ -28,7 +28,7 @@
     "matplotlib",
     "geopandas",
     "flake8>=5.0.0",
-    "time_machine>=2.13.0",
+    "time_machine",
     "pyproj>=3.2.0",  # Pyproj is an optional, best-effort runtime dependency
     "dirty_equals>=0.6.0",
     # (#578) On Python 3.7: avoid dirty_equals 0.7.1 which wrongly claims to be Python 3.7 compatible
diff --git a/tests/extra/test_job_management.py b/tests/extra/test_job_management.py
index 07edafe92..22cc62ca5 100644
--- a/tests/extra/test_job_management.py
+++ b/tests/extra/test_job_management.py
@@ -1,6 +1,7 @@
 import datetime
 import json
 import re
+import sys
 import textwrap
 import threading
 import time
@@ -509,6 +510,11 @@ def test_automatic_cancel_of_too_long_running_jobs(
         cancel_after_seconds,
         expected_status,
     ):
+        if not hasattr(time_machine, "shift"):
+            # TODO #578 remove this hack to skip this test on Python 3.7
+            #       `time_machine.shift` is only available since timemachine>=2.13.0, which only support Python 3.8 and up
+            pytest.skip("time_machine.shift not available")
+
         fake_backend = FakeBackend(requests_mock=requests_mock)
 
         # For simplicity, set up pre-existing job with status "running" (instead of job manager creating+starting it)