Upgrading to Maven 3.1.1 caused Jenkins Maven Job to fail

After upgrading Maven on my Jenkins CI build server to version 3.1.1 (because the android-maven-plugin version 3.8.2 needs it) I encountered  problems with my Maven build jobs in Jenkins (version 1.544).
The error message looks something like this:

 ERROR: Failed to parse POMs  
 ...  
 ...  
 ...  
 Caused by: java.lang.ClassNotFoundException: org.apache.maven.cli.MavenLoggerManager  
      at org.codehaus.plexus.classworlds.strategy.SelfFirstStrategy.loadClass(SelfFirstStrategy.java:50)  
      at org.codehaus.plexus.classworlds.realm.ClassRealm.unsynchronizedLoadClass(ClassRealm.java:259)  
      at org.codehaus.plexus.classworlds.realm.ClassRealm.loadClass(ClassRealm.java:235)  
      at org.codehaus.plexus.classworlds.realm.ClassRealm.loadClass(ClassRealm.java:227)  
      ... 18 more  

Googling around it seems someone else faced the same problem already. He also mentioned Jenkins issue JENKINS-15935 referring to that exact problem.
The solution is to update the Maven Project Plugin in Jenkins because the issue is fixed in Jenkins 1.509.
As of version 2.0 of the plugin, it is released separately but still bundled with Jenkins. Though, it might be the case, that the newest version of the plugin isn't bundled always with the jenkins release.