The Ultimate Edition is the most expensive version of the game, priced at $119.99 (£71.99), and includes exclusive Battlepacks, as well as early access to DLC content.
Multiple posts on the game's Battlelog forum, however, have indicated owners of this version are unable to play the Criminal Activity DLC, while owners of the Standard Edition and Deluxe Edition are unaffected.
Although the content can be downloaded, it is not registering as a validly purchased DLC, according to posts on the forum.
"Ok. it's not downloading it that is the problem, that works fine but once installed it doesn't register as a valid purchased DLC," said one forum user. "When told to do so it says 'no content' under 'My Downloads'."
Multiplayer producer Zach Mumbach has responded to complaints, assuring players that developer Visceral Games is investigating the problems.
"First off, I apologize. This sucks," he said. "Right now we are looking at all the digital versions on PS4 to make sure everyone can download. Best update I can give your right now."