Alex Rodriguez (AP)

Injured pop star Lady Gaga went into hip surgery this week with reassurance from Yankee Alex Rodriguez, who is recovering from the same medical procedure, Page Six has exclusively learned.

Gaga underwent surgery Wednesday to repair the bum hip that’s forced her to cancel the remainder of her world tour, which will reportedly result in up to $30 million in refunds.

We’ve learned that Gaga and A-Rod share the same top surgeon, Dr. Bryan Kelly, at New York’s Hospital for Special Surgery, and were spotted simultaneously arriving at his Manhattan office this week. “Alex was at Dr. Kelly’s office for a follow-up, while Gaga was preparing for surgery,” said a source close to the singer. “It’s natural for anyone to be nervous ahead of this type of surgery, especially as a performer or athlete under tremendous pressure to make a quick recovery and be back at peak performance . . . Gaga was anxious, but Alex talked to her for a while and was able to reassure her.”

The singer, 26, later tweeted she was heading into surgery to treat a labral tear of her right hip, the same injury suffered by A-Rod on his left hip.

No date has been set for Gaga to return to performing, and her management said she would need “strict downtime.” In a post to her fans, she called the setback “a bump in the road,” and explained, “I’ve been hiding a show injury and chronic pain for sometime now.” She added that the injury got so bad she “could not walk.”

As a result, Gaga’s had to cancel dozens of concerts on her Born This Way Ball tour, which raked in $161.4 million last year. She was scheduled to play 22 more dates through March 20.

Meanwhile Rodriguez, 37, is expected to be out till midseason after his Jan. 16 surgery. “I am conducting two rehab sessions each and every day in an effort to get back on the field and rejoin my Yankees teammates,” Rodriguez told The Post Thursday through a spokesman. “I think we have a great team, and I want to be a part of it.”

Reps for Gaga and Rodriguez didn’t get back to us last night.