According to the statement Mandela underwent a procedure via endoscopy to have the gall stones removed at unknown private hospital this morning 15 December 2012 ," it said in a statement.
"The procedure was successful and Madiba is recovering," it added, using the clan name by which Mandela is affectionately known.
According to inside sources Mandela was operated at Medi Clinic Heart Hospital in Pretoria this morning and was later sent back to 1 Military Hospital
"The medical team decided to attend to a lung infection before determining when to attend to the gall stones", the statement from the presidency said.
He was previously hospitalised for an acute respiratory infection in January 2011, when he was kept for two nights.
Mandela has a long history of lung problems dating back decades to when he contracted tuberculosis while in prison.