As the first DLC fighter not part of the game's Season Pass, it was recently announced that Martian Manhunter will be arriving as DLC for Injustice: Gods Among Us on July 30.
Confirmed on the game's U.K. Facebook page yesterday, the post states that Martian Manhunter will be available next Tuesday on the Xbox 360 and PlayStation 3. July 30 is the U.K. date, but the North American release should be right around that. As for the Wii U version, there's been no date announced.
Netherrealm Studios hasn't given a price for the Martian Manhunter DLC, but previous characters could be bought for $5 (400 Microsoft Points) if you didn't have the Season Pass.