Granderson, out since May 24 with a fractured left pinkie finger, made three plate appearances and ran the bases. He drew two walks and put the ball in play once, hitting a weak grounder to second base. The 32-year-old outfielder also fielded fly balls in the outfield before the sim game.
"I'm at the Spring Training point again, in terms of the schedule to hit," said Granderson, who has played in only eight games for the Yankees this season. "This is like the first couple of days before the first Spring Training game. I need some swings right now. That's the main thing I'm missing."
Granderson was pleased with how he felt physically and said he is scheduled to take part in two more sim games -- Tuesday and Wednesday -- before the Yankees re-evaluate how close he is to starting a Minor League rehab assignment. He isn't sure, however, exactly when he'll be back in the Bronx.
"Sooner than later," Granderson said. "I got a lot of friends and family asking the same question. We're getting there, which is always a good thing."
Infielder Jayson Nix took six simulated at-bats along with Granderson, recording two singles and two strikeouts, but he did not run the bases to test his strained right hamstring.
Catcher Francisco Cervelli, meanwhile, went through defensive drills on the back fields. Cervelli has been sidelined since April 26, when he sustained a right hand fracture on a foul tip. The 27-year-old backstop has not taken batting practice since a setback in his recovery, a stress reaction in his right elbow, but he said that is "coming soon."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. Adam Berry, a reporter for MLB.com, contributed to this story from Tampa, Fla. This story was not subject to the approval of Major League Baseball or its clubs.