diff --git a/rest_framework/__init__.py b/rest_framework/__init__.py
index c0b5c4c04..967f87019 100644
--- a/rest_framework/__init__.py
+++ b/rest_framework/__init__.py
@@ -6,6 +6,7 @@ ______ _____ _____ _____    __
 | |\ \| |___/\__/ / | |   | | | | | (_| | | | | | |  __/\ V  V / (_) | |  |   <
 \_| \_\____/\____/  \_/   |_| |_|  \__,_|_| |_| |_|\___| \_/\_/ \___/|_|  |_|\_|
 """
+import checks  # NOQA
 
 __title__ = 'Django REST framework'
 __version__ = '3.6.3'
diff --git a/rest_framework/checks.py b/rest_framework/checks.py
new file mode 100644
index 000000000..96d6f4237
--- /dev/null
+++ b/rest_framework/checks.py
@@ -0,0 +1,20 @@
+from django.core.checks import Tags, Warning, register
+
+
+@register(Tags.compatibility)
+def pagination_system_check(app_configs, **kwargs):
+    errors = []
+    # Use of default page size setting requires a default Paginator class
+    from rest_framework.settings import api_settings
+    if api_settings.PAGE_SIZE and not api_settings.DEFAULT_PAGINATION_CLASS:
+        errors.append(
+            Warning(
+                "You have specified a default PAGE_SIZE` pagination rest_framework setting,"
+                "without specifying also a `DEFAULT_PAGINATION_CLASS`.",
+                hint="The prior version of rest_framework defaulted this setting to "
+                "`PageNumberPagination` however pagination defaults to disabled now.  "
+                "Consider specifying `DEFAULT_PAGINATION_CLASS` explicitly for your project, "
+                "unless you specify individual pagination_class values on specific view classes.",
+            )
+        )
+    return errors
diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index 0b6155942..0255cfc7f 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -5,7 +5,6 @@ be used for paginated responses.
 """
 from __future__ import unicode_literals
 
-import warnings
 from base64 import b64decode, b64encode
 from collections import OrderedDict, namedtuple
 
@@ -147,17 +146,6 @@ PAGE_BREAK = PageLink(url=None, number=None, is_active=False, is_break=True)
 class BasePagination(object):
     display_page_controls = False
 
-    def __init__(self, *args, **kwargs):
-        # Use of default page size setting requires a default Paginator class
-        if api_settings.PAGE_SIZE and not api_settings.DEFAULT_PAGINATION_CLASS:
-            warnings.warn(
-                "A valid paginator class must be specified with `DEFAULT_PAGINATION_CLASS` "
-                "when using the `PAGE_SIZE` default pagination setting."
-                "Defaulting the setting to specifies `PageNumberPagination` "
-                "is deprecated as pagination is  disabled by default.",
-                DeprecationWarning
-            )
-
     def paginate_queryset(self, queryset, request, view=None):  # pragma: no cover
         raise NotImplementedError('paginate_queryset() must be implemented.')