The 26-year-old Scot gave the thumbs up sign lying in his hospital bed in a picture he posted on his Twitter account to show he was in good spirits after the operation.
The world number three announced last week that he had decided to have a minor operation to sort out a disc problem in his lower back that has been bothering him for most of this year.
That means it is unlikely he will play again this year missing the last four tournaments of the season in Asia, Paris and the World Tour Finals in London.
On Monday night, Murray posted on Twitter: "Thanks for all the well wishes, means a lot to me..." alongside the photo of him lying in a hospital bed with both thumbs up.
The 26-year-old added: "First thing I said when I came round was "did I win?" #somethingsneverchange."
The back issue that Murray has battled with flared up badly in May during the Rome Masters, prompting him to abandon a second-round match against Marcel Granollers and pull out of the French Open.
While he played a full role in Great Britain qualifying for the elite World Group of the Davis Cup with victory in Croatia, there were concerns that his back was giving him trouble.
However, Murray won two singles matches and partnered Colin Fleming to a doubles victory as Great Britain defeated Croatia 4-1 in Umag.
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