The 22-year-old safety will be replaced in the Giants' line-up by Tyler Sash after testing positive for banned drug Adderall.
NFL: Four match ban for New York Giants' Hill after failing drugs test
The 22-year-old rookie, who has made 11 tackles in five games this season for the club, will be eligible to return on November 5 - a day after the Giants face the Pittsburgh Steelers.
Hill claimed the violation came as a result of a prescription substance he took before joining the Giants and his lack of knowledge about the NFL's banned substances.
"I received a doctor's prescription for Adderall prior to signing with the Giants," Hill said. "Shortly after signing with the team, I was in a meeting with (director of player development) Charles Way, who reviewed the list of the league's banned substances. I knew at that point that this may be an issue.
"I was tested and the results came back that Adderall was in my system. I appealed but lost the appeal. I accept full responsibility for this situation, and it won't happen again.
"The Giants have given me a great opportunity when nobody else would, and I don't take that for granted. I feel badly this has happened. I will work hard and stay in great shape these next four weeks so I can come back and contribute to this team after my suspension."
The Giants have added defensive back Tyler Sash to the roster to replace Hill - after Sash finished his own four-match suspension for testing positive for Adderall.
Meanwhile Arizona Cardinals running back Ryan Williams will miss the rest of the season with a shoulder injury.
The 22-year-old suffered damage to his left shoulder on a hard hit during the fourth quarter of Arizona's 17-3 loss to the St. Louis Rams, and will undergo surgery later this week.
"It's a tough thing for Ryan," said Ken Whisenhunt, the Cardinals coach.
"The timetable for recovery is probably three months, so that puts him out for the season.
"We didn't think after the game it was going to be the case, but in getting tests done on it and talking to the doctor, it's something that's going to require surgery."
Williams, who lay motionless on the field for several minutes after being hit by Rams safety Darian Stewart, missed all of his rookie season in 2011 after rupturing his patellar tendon during the preseason.
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