Rodriguez, 32, was diagnosed after an MRI was taken at Columbia Presbyterian Medical Center in New York. He had played in four consecutive games after jumping back into the lineup on Friday against the Indians, but was removed for a pinch-hitter on Monday at Cleveland and said there was "no way" he could play on Tuesday at Yankee Stadium.
Girardi characterized the injury as "surprising" to the Yankees, who also have catcher Jorge Posada on the disabled list for the first time in his big league career.
Rodriguez went 2-for-13 with a walk in the weekend series at Cleveland, rejoining the team after he was originally injured running out a fielder's choice in an April 20 game at Baltimore.
"Grade 2 puts him down for the 15 days," Yankees general manager Brian Cashman said. "If it's longer and it needs longer, so be it. We've just got to make sure we get it right so we can get him going again."
The Yankees have not yet officially executed the disabled list move for Rodriguez, but are expected to do so before Wednesday's game against Detroit. Cashman said the Yankees would recall a pitcher from Triple-A Scranton/Wilkes-Barre to temporarily help out the bullpen after Ross Ohlendorf threw 3 1/3 innings in relief of an ineffective Phil Hughes on Tuesday.
Rodriguez's injury was similar to the strained left quadriceps suffered by Yankees shortstop Derek Jeter earlier this month, costing Jeter six games. Rodriguez flew home to Miami after the April 20 game to witness the birth of his second daughter and received treatment there, but was back in the lineup after missing just three games.
Cashman said that he was not sure if Rodriguez had rushed back into the lineup, saying, "He'd be the only one that can answer that."
Rodriguez was not available for comment after Tuesday's game, but speaking in Cleveland on Monday, he hinted that he may have hurried too much.
"I had a quad injury like this my senior year in high school, and it lingered on for a couple of months," Rodriguez said. "It's important to get it right. I think Jeter took the right approach where he took a little bit more time. That's probably what I need, too."
Cashman said that Rodriguez will stay with the team until further notice and continue to receive treatment. He will not be shut down completely, as the Yankees' main concern is keeping him from the explosive nature of running at 95 to 100 percent.
"He can do a lot of functional things," Cashman said. "It's just that last 'oomph' would put him at major, major risk to make it worse. He can't function at full capacity with it."
In his absence, the Yankees can continue to use Morgan Ensberg (.233, 1 HR, 3 RBIs in 43 at-bats) or Alberto Gonzalez (.316, 1 HR, 2 RBIs in 19 at-bats) at third base.
Cashman also said that Wilson Betemit, on the disabled list since April 14 with a corneal ulcer, was cleared by an eye doctor on Tuesday to resume playing. Betemit is expected to join Scranton/Wilkes-Barre for a rehab assignment beginning Thursday.
Rodriguez -- in the first year of a 10-year contract that could be worth as much as $300 million -- is batting .284 with four home runs and 11 RBIs in 24 games. The disabled list assignment is the fifth of his career and his first with the Yankees, having last been on the DL from July 8-24, 2000 (right knee strain) while with the Seattle Mariners.
"He's a hard guy to replace, but we have a lot of good players in this organization," Girardi said. "You've just got to find a way to get it done. It's unfortunate we're not going to have him for two weeks, but we've got to find a way."