"Today I underwent successful right hip surgery at the St Vincent Hospital in Melbourne," the former world number one said on Facebook. "I'd like to thank Dr John O'Donnell and all of the staff for looking after me. I look forward to returning to competitive tennis during the grasscourt season. Thanks to everyone for all the well wishes and support over the last few days. I'll come back from this."
The three-time Grand Slam champion, who dislodged Novak Djokovic from the top of the rankings towards the end of 2016, has slipped to 19th in the world due to his lengthy lay-off. He first felt pain in his right hip during his French Open semi-final loss to Swiss Stan Wawrinka in June.
The grasscourt season starts after the French Open, with the first event taking place in Stuttgart, Germany, from June 11. Murray is a two-time Wimbledon winner and has been champion at Queen's in London on five occasions, both of which are played on grass courts.
The BBC reported that he hopes to be hitting balls on court in about seven or eight weeks and has been given a timescale of 14 weeks as a guide for a return. But Murray said he is not "interested in coming back for a specific tournament", in comments reported by the BBC.
"My plan is to be back playing around the grass-court season - potentially before then - but I'm certainly not going to rush anything," he said. "I want to know when I come back that I'm ready."