Murray, 31, underwent right hip surgery in January. Dr. John O'Donnell performed the surgery at St. Vincent Hospital in Melbourne, Australia.
Dr. Derek Ochiai -- a sports medicine expert based in Arlington, Va. -- said that the typical recovery for Murray's injury is up to one year. Murray began his 2018 season with a loss to Nick Kyrgios in the round of 32 at June's Fever-Tree Championships. A week later, he made it into the round of 16 at the Nature Valley Invitational.
Murray advanced into the quarterfinals at the 2018 Citi Open, but pulled out of his match against Alex de Minaur following a three-hour match against Marius Copil, which lasted until after 3 a.m. Murray experienced several other delays at the tournament, with his first match being delayed by rain and not starting until after 10 p.m.
He also withdrew from this week's Rogers Cup. There are just two more tournaments before the U.S. Open: the Western & Southern Open and the Winston-Salem Open.
"I won't be able to play my match tonight," Murray said in a statement Friday on the ATP website. "I'm exhausted after playing so much over the last [four] days, having not competed on the hard courts for 18 months. I also need to be careful and to listen to my body as I come back from a long-term injury. I'm gutted not to be playing, and I'd like to thank the tournament and all the fans. There are lots of positives to take from this week, so I'll take some time to rest and recover ... and then head to Cincinnati early to prepare and get ready."
Ochiai said athletes can usually resume playing their sport again about three months after surgery, but they aren't a "ball of fire" when they return.
"You may be able to physically play, but a lot of times with these type of injuries with the hip, it's like the center of a wheel," Ochiai said. "It's like the central part in your lower extremities. So all of these muscles connect around the hip ... you start getting changes in how you move and relearning how to move normally, that takes a long time."
Murray, 31, has been posting videos of his workouts to social media since dropping out of the tournaments. He appears to be working on his lateral movement and flexibility.
The 2018 U.S. Open begins on Aug. 27 at the USTA Billie Jean King National Tennis Center in New York City.
"Unless they are a Grand Slam, [the small tournaments] are only three-set matches," Ochiai said. "The Grand Slam, every match is 40 percent on average longer. So that could be more pressure on the hip. He's going to be able to handle non Grand Slam tournaments to be feel comfortable and confident with the hip before he is ready for a Grand Slam."