"The surgery went as planned and without complication," the team said in a statement.
Rodriguez is expected to miss the first half of the 2013 season. His hip problem was diagnosed in November after he had gone 3-for-25 with 12 strikeouts during playoff series against Baltimore and Detroit.
Because of the injury, Rodriguez was unable to rotate his hips -- thus causing a lack of power at the plate.
The surgery was Rodriguez' second in five years. He had his right hip repaired prior to the 2009 season.
"I have full confidence that between the operating physician and the patient, whose work ethic is legendary, that this will all work out over time," New York General Manager Brian Cashman said. "But right now, time is a problem. We're going to be missing him for some time. We will deal with that."