How to move installed modules from /sites/all/modules/* to /sites/all/contrib/modules/*
You only need to move your modules to the your new location and rebuild the regisry. When the registry rebuilds the path to the modules will be updated. Check registry_rebuild(). 


  Rescans all code in modules or includes directories, storing the location of each interface or class in the database.


Although, I would recommend you to backup you database before testing this.

If you are using drush you could also rebuild the registry using the following command:

drush cc registry


You can also install the registry_rebuild command for drush:

// install registry_rebuild
drush dl registry_rebuild
// rebuild the registry
drush rr