Yankees manager Joe Girardi said that he thought Rodriguez, considered a quick healer, historically, could be back in the minimum time. The disabled list assignment is Rodriguez's first as a Yankee and his first since 2000 with the Mariners.
"None of us know exactly, but my thought is 15 days," Girardi said. "I believe that he'll be back in 15 days."
In an immediate move, the Yankees recalled right-hander Chris Britton from Triple-A Scranton/Wilkes-Barre to take Rodriguez's roster spot, but that is believed to be a temporary fix to help out the bullpen after Phil Hughes lasted less than four innings on Tuesday.
In the meantime, the Yankees will go forward with Morgan Ensberg and Alberto Gonzalez as their third basemen on the Major League roster, though Rodriguez -- batting .284 with four home runs and 11 RBIs in 24 games -- will be missed.
"It's painful to see that lineup without me in the cleanup spot and helping my team win every day," Rodriguez said. "Me being a right-handed hitter, it's a great complement to all of our lefties. We're so left-handed dominant. [Jorge] Posada is an incredible right-handed hitter, so now we've got two guys out. It takes it off the balance of our lineup, but at the same time, I think we've got guys who are capable of picking up the slack."
"These are the types of guys that are hard to replace, and we all know that," Girardi said.
Rodriguez was diagnosed with a Grade 2 strain of his right quadriceps on Tuesday. He 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.
Rodriguez, who said he also had a serious quad strain while in high school that persisted for months, believes he made the injury worse by rushing back after just three games.
"I think I went from a [Grade] 1 to a 2 on the ground ball to second in Cleveland [on Monday]," Rodriguez said. "If you're asking me if I can play tonight, I'll play tonight. I'll go out there until I'm dead. ... I wanted to play. I begged to get in there. They gave me every chance to sit down if I wanted to."
Though shortstop Derek Jeter missed six games with a left quad strain and has shown no ill effects, Girardi said that the Yankees had discussed Rodriguez's situation and believed he was ready to play on Friday at Progressive Field.
Rodriguez ran a few pass patterns through the outfield on Friday in front of Girardi and the Yankees' medical staff, playing catch with bench coach Rob Thomson. Girardi watched for only a few minutes before announcing, "He's in the lineup."
"We talked about it, all of us -- doctors, trainers, general manager and me," Girardi said. "Alex felt that he was ready to come back. We told Alex just to take it slow. In hindsight, maybe he wasn't as ready as he felt. You talk to everyone and everyone was in agreement that we thought he was ready."
Rodriguez is expected to remain with the team while they play out a nine-game homestand, receiving whirlpool treatment as well as ice and heat, and the team will decide on the next move from there.
Rodriguez did not rule out the possibility that he would eventually have to go on a Minor League rehabilitation assignment, but said the difficult part now would be watching as the 14-14 Yankees continue on without him.
"It's very tough," Rodriguez said. "We're at a time now when we need a full roster. Part of my responsibility is to be out there every day. My biggest goal coming in every year is to play 162. It's a very upsetting situation to me."