The former No. 1-ranked Murray, a three-time major winner, has not played a competitive match since a quarterfinal exit at Wimbledon last July.
Murray has been told to expect a 14-week recovery period and he is targeting a return to the court by June.
“I underwent successful right hip surgery at the St Vincent Hospital in Melbourne,” Murray wrote on his Facebook page. “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 grass court season. Thanks to everyone for all the well wishes and support over the last few days. I’ll comeback from this.”
The 30-year-old Murray, though, accepts he will have to reduce his workload on court.
“I’m certainly not going to be putting in the same amount of tournaments and effort to try to get to No. 1,” Murray told British media. “I’ll certainly be more considered in the amount of tournaments I play, even though I play a conservative schedule anyway in comparison to most of the players on the tour.
“I’ll be playing a reduced schedule, and then focusing more on trying to win major events and big tournaments rather than trying to achieve certain ranking goals.”
Murray said he can get himself back to “95 percent of my best.”
“I believe that’s enough to compete at the highest level,” he added. “No question.”