Mino Raiola said in a statement about the surgery that the 35-year-old’s ACL problem was not a "career-ending injury".
The Swede sustained "significant knee ligament damage" in Manchester United's 2-1 Europa League victory over Anderlecht last month and was ruled out for the rest of the season.
Ibrahimovic had the surgery at the University of Pittsburgh Medical Center.
"Zlatan Ibrahimovic has undergone successful knee surgery. He will make a full recovery and has not suffered a career-ending injury," the statement read.
"The procedure was performed by Freddie Fu, M.D, and Volker Musahl, M.D, of the UPMC Sports Medicine program in Pittsburgh.
"Zlatan has started rehabilitation at UPMC and will remain under the care of Dr. Fu and Dr. Musahl throughout his recovery.
"Zlatan and the medical team are not available for interviews at this time. Additional updates will follow at a later date."
Ibrahimovic, whose United contract runs out in the summer, has vowed to come back stronger and has said that "giving up is not an option", despite United boss Jose Mourinho suggesting that recovery would be "really, really hard" given Ibra’s age.
The former Barcelona star joined United last summer from Paris Saint-Germain and has been a big success in his debut season, scoring 28 goals in 46 appearances.