Hosley will be banned, without pay, after violating the league's substance-abuse policy.
The news comes as a further blow to the Giants, with safety Will Hill handed a six-game suspension earlier this week.
Hill's ban led to his release from the team, although Hosley has not yet been cut from the roster.
Hosley has made just seven career starts since joining the Giants, who chose him in the third round of the 2012 NFL Draft.
After leaving the Virginia Tech Hokies in 2012, Hosley failed a drugs test at the NFL Scouting Combine.