Rodriguez had surgery March 9 in Vail, Colo., to remove an impingement in the joint and drain a cyst in the hip.
He said Rodriguez would stretch, do agility work, light jogging, take some grounders, hit off a tee and take soft toss swings on Monday.
"He has long days," Girardi said. "It is not like normal spring training where you show up for a couple of hours and you go home."
With the Yankees opening a series Monday night at Tampa Bay, Girardi said he expects Rodriguez to be at the game.
Rodriguez hit .302 with an American League-leading .573 slugging percentage last season. The three-time MVP is expected to return to the lineup in May.
"So much depends on how he feels the next day, if he has a setback," Girardi said. "It will be awhile."
First baseman Mark Teixeira, who signed a $180 million, eight-year contract with the Yankees in the offseason, was held out of the lineup Sunday for the second consecutive game with tendinitis in his left wrist.
"He is still sore, so I didn't see any reason to play him," Girardi said. "Tendinitis sometimes takes some time to get out, so he's got to work out that soreness. The diagnosis was good, but you never know how long it takes to get it out."