Sash, a 2011 sixth-round draft pick from Iowa, will forfeit four game checks. He will be eligible to return to the Giants' active roster on Oct. 1 following the team's Week 4 game against the Philadelphia Eagles.
Sash, however, will be allowed to participate in training camp and all four preseason games.
Sash said he tested positive for the medication Adderall in March, according to the New York Daily News.
"I had no idea this prescription drug was banned by NFL policy," Sash said in a statement to the newspaper, adding that he was taking the drug "under a doctor's care for an anxiety condition."
The safety appeared in all 16 regular season games last season as a rookie. He recorded 17 tackles and forced one fumble. Sash had seven postseason tackles during the Giants' march to winning Super Bowl XLVI.