Four other Seals are under investigation.
They are alleged to have divulged classified information to the maker of a video game called Medal Of Honor: Warfighter.
The seven received a punitive letter of reprimand and a partial forfeiture of pay for two months. Those actions generally hinder a military member's career.
The deputy commander of Naval Special Warfare Command, Rear Admiral Garry Bonelli, acknowledged nonjudicial punishments had been handed out.