A senior defence official said the troops received what the military calls "non-judicial" punishment.
They are said to have provided the information to the maker of a video game.
The official said four other SEALs were being investigated for similar alleged disclosures.
Each of the seven received a punitive letter of reprimand and a partial forfeiture of pay for two months – actions that generally hinder a military member's career.
The deputy commander of Naval Special Warfare Command, Rear Admiral Garry Bonelli, acknowledged that non-judicial punishments had been handed out for misconduct, but did not say any more.
The commandos are alleged to have divulged classified information to the maker of a video game called Medal of Honour: Warfighter.
The two main complaints against the SEALs were that they did not seek the permission of their command to take part in the video project and that they showed the video designers some of their specially designed combat equipment.
SEALs are obliged to sign non-disclosure agreements when they enter service and when they leave.