This is the second time Hill has been banned by the NFL. Last season, Hill served a four-game suspension for violating the league's performance-enhancing substances policy. Hill said he took the attention deficit drug Adderall.
Hill, 23, is eligible to return to the active roster on Sept. 30 after the Giants play the Chiefs. The second-year safety is eligible to participate in preseason practices and games.
The Giants are expecting stiff competition at safety in training camp. Antrel Rolle and Stevie Brown are going to start but Ryan Mundy, Hill, fifth-round pick Cooper Taylor and Tyler Sash are all competing for roles and roster spots behind the two starters.
Giants backup wide receiver Brandon Collins was also suspended for the first four games of the season last month for violating the NFL Policy and Program for Substances of Abuse.
The Giants have their first camp practice next Saturday in East Rutherford, N.J.