The Wii and Xbox 360 versions of the dance title initially launched in November 2011, but a port was also being developed for the iPhone and iPad.
Although Ubisoft has spent $233,000 (£144,000) on the iOS project, the developer is apparently unable to release the game as the Black Eyed Peas have yet to respond to approval requests, reports Eurogamer.
Legal documents state: "Since March 2012, and despite Ubisoft's repeated requests, BEP Music has breached the contract by failing and refusing to either approve or disapprove the IOS game in writing or otherwise.
"Ubisoft has performed all of the obligations required of it under the contract, except as those obligations that have been excused by BEP Music's conduct or by operation of law."
The company is suing for $1m to cover development costs as well as ongoing lost profits.
> Read Digital Spy's review for The Black Eyed Peas Experience
Watch a trailer for The Black Eyed Peas Experience below: