Murray, 30, who has not played competitively since last year's Wimbledon, made the announcement on his Facebook page hours after the surgery and says he is confident he will return as strong as before.
Murray lost to Sam Querrey in his last competitive match, back at Wimbledon in 2017, and despite planning on making his long-awaited return Down Under, those plans were scuppered. Despite a couple of seemingly positive exhibitions in the past couple of weeks, Murray admitted defeat last Thursday when he pulled out of the Australian Open.
He was operated on by Dr John O'Donnell at the St Vincent Hospital in Melbourne on Monday.
There is no current update on when Murray could possibly return to competitive tennis. Thanks to everyone for the well wishes and support the last few days. "I'll come back from this".
Murray will be a big miss Down Under in Australia, but with his hip causing him problems since the summer, it's probably wise that he's sitting it out.
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"I'm very optimistic about the future - the surgeon is very happy about how it went". One of the things that I would like to do is play until my eldest daughter is able to watch me and have a small understanding of what it is I've done for my living.
Murray also said he underwent some minor surgery on his groin on 18 December. "I'm going to be competing at the highest level again", Murray was quoted as saying by the BBC.
The former world number one was previously expected and confirmed to take part in Melbourne for the 2018 Australian Open.
"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 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", he said.
"So if I can get myself to 95% of my best, I believe that's enough to compete at the highest level".
"That would be cool if she can come along and watch me hit some balls or practice just to see what it is I do", he said.