Now why would you want to do this? If you do not feel confident upgrading some plugins which may not link to the core update or your theme and may cause problems, this is a great way to remove those annoying red notifications.
To remove the notifications all you need to do is install this plugin: Disable WordPress Plugin Updates
Want to remove all notifications? Theme, core and plugins updates? Simply install this plugin: Disable All WordPress Updates
By activating this plugin all theme, core and plugin update notifications are disabled. If you want to have a quick look if new versions are existing, simply deactivate this plugin for a short time.