The FFI suspended Persepolis defender Mohammad Nosrati for 10 months and his teammate Sheys Rezaei for 20 months, ISNA news agency reported.
The FFI also imposed a cash fine of 30,000 dollars on the two players, the report added.
Nosrati had grabbed the backside of his teammate Rezaei while celebrating his team's goal in a league game last month against Damash Gilan which was broadcast live on state television.
The team had already cut both players' salaries by 15 percent although Nosrati testified that the gesture was accidental rather than intentional.
Nosrati, 30, has been on the national team for 11 years and scored the goal that put Iran into the 2006 World Cup in Germany.
