Authorities told the Atlanta Journal-Constitution they are searching for the man for questioning concerning the Sunday shooting.
Gilmer County Sheriff Stacy Nicholson said the incident occurred at a residence after an argument started between acquaintances.
The two male victims were airlifted to Atlanta Medical Center with wounds to the head. Nicholson said one of the men was seriously injured.
Nicholson said the injured woman was taken to North Georgia Medical Center in Ellijay by the man wanted for questioning.
Police said the man left the hospital on foot. The hospital was put on temporary lock-down.