diff --git a/heat/engine/constraint/common_constraints.py b/heat/engine/constraint/common_constraints.py
index 427342447e..5588ef7128 100644
--- a/heat/engine/constraint/common_constraints.py
+++ b/heat/engine/constraint/common_constraints.py
@@ -14,7 +14,13 @@
 import croniter
 import eventlet
 import netaddr
-import pytz
+
+try:
+    import zoneinfo
+except ImportError:
+    # zoneinfo is available in Python >= 3.9
+    import pytz
+    zoneinfo = None
 
 from neutron_lib.api import validators
 from oslo_utils import timeutils
@@ -167,7 +173,10 @@ class TimezoneConstraint(constraints.BaseCustomConstraint):
         if not value:
             return True
         try:
-            pytz.timezone(value)
+            if zoneinfo:
+                zoneinfo.ZoneInfo(value)
+            else:
+                pytz.timezone(value)
             return True
         except Exception as ex:
             self._error_message = _(
diff --git a/heat/tests/clients/test_swift_client.py b/heat/tests/clients/test_swift_client.py
index ae04ae42c9..8ad43f7ad1 100644
--- a/heat/tests/clients/test_swift_client.py
+++ b/heat/tests/clients/test_swift_client.py
@@ -14,7 +14,13 @@
 import datetime
 from unittest import mock
 
-import pytz
+try:
+    import zoneinfo
+except ImportError:
+    # zoneinfo is available in Python >= 3.9
+    import pytz
+    zoneinfo = None
+
 from testtools import matchers
 
 from heat.engine.clients.os import swift
@@ -126,8 +132,12 @@ class SwiftUtilsTest(SwiftClientPluginTestCase):
 
     def test_parse_last_modified(self):
         self.assertIsNone(self.swift_plugin.parse_last_modified(None))
+        if zoneinfo:
+            tz = zoneinfo.ZoneInfo('GMT')
+        else:
+            tz = pytz.timezone('GMT')
         now = datetime.datetime(
-            2015, 2, 5, 1, 4, 40, 0, pytz.timezone('GMT'))
+            2015, 2, 5, 1, 4, 40, 0, tz)
         now_naive = datetime.datetime(
             2015, 2, 5, 1, 4, 40, 0)
         last_modified = now.strftime('%a, %d %b %Y %H:%M:%S %Z')
diff --git a/heat/tests/constraints/test_common_constraints.py b/heat/tests/constraints/test_common_constraints.py
index c466b06054..03399bf691 100644
--- a/heat/tests/constraints/test_common_constraints.py
+++ b/heat/tests/constraints/test_common_constraints.py
@@ -13,6 +13,12 @@
 
 from unittest import mock
 
+try:
+    import zoneinfo
+except ImportError:
+    # zoneinfo is available in Python >= 3.9
+    zoneinfo = None
+
 from heat.engine.constraint import common_constraints as cc
 from heat.tests import common
 from heat.tests import utils
@@ -279,7 +285,10 @@ class TimezoneConstraintTest(common.HeatTestCase):
 
     def test_validation_error(self):
         timezone = "wrong_timezone"
-        expected = "Invalid timezone: '%s'" % timezone
+        err = timezone
+        if zoneinfo:
+            err = "No time zone found with key %s" % timezone
+        expected = "Invalid timezone: '%s'" % err
 
         self.assertFalse(self.constraint.validate(timezone, self.ctx))
         self.assertEqual(
diff --git a/heat/tests/openstack/aodh/test_alarm.py b/heat/tests/openstack/aodh/test_alarm.py
index 48b756fddb..609cc9dc26 100644
--- a/heat/tests/openstack/aodh/test_alarm.py
+++ b/heat/tests/openstack/aodh/test_alarm.py
@@ -16,6 +16,12 @@ import copy
 import json
 from unittest import mock
 
+try:
+    import zoneinfo
+except ImportError:
+    # zoneinfo is available in Python >= 3.9
+    zoneinfo = None
+
 from heat.common import exception
 from heat.common import template_format
 from heat.engine.clients.os import aodh
@@ -579,11 +585,14 @@ class AodhAlarmTest(common.HeatTestCase):
             exception.ResourceFailure,
             scheduler.TaskRunner(rsrc.update, snippet)
         )
+        err = timezone
+        if zoneinfo:
+            err = "No time zone found with key %s" % timezone
         self.assertEqual(
             "StackValidationFailed: resources.MEMAlarmHigh: Property error: "
             "Properties.time_constraints[0].timezone: Error "
             "validating value '%s': Invalid timezone: '%s'"
-            % (timezone, timezone),
+            % (timezone, err),
             error.message)
 
     def test_alarm_live_state(self):
diff --git a/requirements.txt b/requirements.txt
index 04ebf4e9e9..f25280dcc9 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -51,10 +51,11 @@ python-troveclient>=2.2.0 # Apache-2.0
 python-vitrageclient>=2.7.0 # Apache-2.0
 python-zaqarclient>=1.3.0 # Apache-2.0
 python-zunclient>=3.4.0 # Apache-2.0
-pytz>=2013.6 # MIT
+pytz>=2013.6;python_version<"3.9" # MIT
 PyYAML>=5.1 # MIT
 requests>=2.23.0 # Apache-2.0
 tenacity>=6.1.0 # Apache-2.0
+tzdata>=2022.4;python_version>="3.9" # MIT
 Routes>=2.3.1 # MIT
 SQLAlchemy>=1.4.0 # MIT
 stevedore>=3.1.0 # Apache-2.0