The Swedish striker had suffered a season-ending knee ligament injury in the 2-1 Europa League win over Anderlecht at Old Trafford last month. The recent injury has cast doubts over the striker's future at the club.
Ibrahimovic's agent, Mino Raiola, released a statement to confirm that his client hasn't suffered a career-ending injury.
"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."
Ibrahimovic is unlikely to receive a contract extension from United and sources believe he may be headed to MLS.