Hill is the second Giants safety to be suspended for using the drug. Safety Tyler Sash served a four-game suspension for using Adderall as well. Sash was activated on Monday and takes Hill's roster spot.
Hill's suspension is effective immediately and he will not be eligible to return until Nov. 5.
"I received a doctor's prescription for Adderall prior to signing with the Giants," Hill said in a statement. "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," he added. "I appealed but lost the appeal. I accept full responsibility for this situation, and it won't happen again."
Sash said he had a prescription for Adderall to help combat anxiety over public speaking during the offseason. He appealed and lost as well.
However, the NFL suspended running back Andre Brown for using the same drug earlier this year but Brown appealed and had his suspension overturned. Brown said he took Adderall, commonly prescribed for attention-deficit hyperactivity disorder, and that the suspension came from a misunderstanding over paperwork.
Hill signed with the Giants as a free agent on May 14 after impressing in rookie minicamp. He went undrafted in 2011 after coming out of Florida early. Teams reportedly stayed away from him due to character concerns.
The safety has played in all five games and has seven tackles. He forced a fumble on a kickoff return against Cleveland during Sunday's 41-27 victory.
"The Giants have given me a great opportunity when nobody else would, and I don't take that for granted," Hill said. "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."