diff --git a/lib/ansible/modules/packaging/os/dnf.py b/lib/ansible/modules/packaging/os/dnf.py
index d8c2e14787e..02dc9edb66a 100644
--- a/lib/ansible/modules/packaging/os/dnf.py
+++ b/lib/ansible/modules/packaging/os/dnf.py
@@ -464,10 +464,10 @@ class DnfModule(YumDnf):
 
     def _ensure_dnf(self):
         if not HAS_DNF:
-            if PY2:
-                package = 'python2-dnf'
-            else:
+            if not PY2:
                 package = 'python3-dnf'
+            else:
+                package = 'python2-dnf'
 
             if self.module.check_mode:
                 self.module.fail_json(
diff --git a/test/integration/targets/dnf/tasks/main.yml b/test/integration/targets/dnf/tasks/main.yml
index aba860fe5a1..92e35611ebb 100644
--- a/test/integration/targets/dnf/tasks/main.yml
+++ b/test/integration/targets/dnf/tasks/main.yml
@@ -43,3 +43,7 @@
   when:
     - ansible_distribution == 'Fedora' and ansible_distribution_major_version|int >= 29
     - ansible_distribution == 'RedHat' and ansible_distribution_major_version|int >= 8
+
+- include: 'python3and2.yml'
+  when:
+    - ansible_pkg_mgr == 'dnf'
diff --git a/test/integration/targets/dnf/tasks/python3and2.yml b/test/integration/targets/dnf/tasks/python3and2.yml
new file mode 100644
index 00000000000..dd59b90f2b7
--- /dev/null
+++ b/test/integration/targets/dnf/tasks/python3and2.yml
@@ -0,0 +1,44 @@
+# INSTALLPYTHON3AND2
+#  The module `dnf` installs python3-dnf on python3 systems and python2-dnf
+#  on python2 systems. Fedora 30 and newer have python3 and limited
+#  support for python2, for example python2-dnf is missing.
+#  This test proves that python3 and python2 can be installed and the module
+#  `dnf` works.
+
+- name: install python2
+  dnf:
+    name: python2
+    state: present
+
+- name: use python2
+  set_fact:
+    ansible_python_interpreter: /usr/bin/python
+
+- name: install a sample package
+  dnf:
+    name: screen
+    state: present
+
+- name: clean up sample package
+  dnf:
+    name: screen
+    state: absent
+
+- name: install python3
+  dnf:
+    name: python3
+    state: present
+
+- name: use python3
+  set_fact:
+    ansible_python_interpreter: /usr/bin/python3
+
+- name: install a sample package
+  dnf:
+    name: screen
+    state: present
+
+- name: clean up sample package
+  dnf:
+    name: screen
+    state: absent