This was confirmed by a Facebook spokeswoman who released a statement saying, “Yes, we’re now allowing people to upload and share files within Facebook Groups […] We first introduced this feature a few months ago with Groups at Schools. Now, we’re making it more widely available. It’ll roll out to more groups over the course of the coming days and all groups should have it soon.”
No word on if there is a limit to how many files can be shared, but each file size will be limited to 25MB. Head on over to one of your Facebook Groups to see if the feature has been rolled out to you yet.