The 32-year-old outfielder suffered a strained right oblique muscle while taking batting practice on Monday and is expected to be sidelined for two to three weeks of action.
"It was painful," Abreu said Tuesday. "You just have to hang with it, and don't try to worry about too much. It's sore. I felt a little pain there and thought it was nothing to worry about. I kept swinging and then, after one swing, [I felt] a big pain."
Abreu, who batted .297 with 15 home runs and 107 RBIs last season for the Phillies and Yankees, is projected as New York's starting right fielder.
He expects to return to action in mid-March and will be available for the Yankees' regular season opener on April 2, suggesting that his recovery could take as little as 10 days.
"I'm just doing treatment right now and just trying to get better," Abreu said. "I don't think it'll take that long. I'll take a couple of weeks, just get treatment and I think I'm going to be ready for the season."
Yankees manager Joe Torre said on Monday that Abreu would be limited to basic cardiovascular exercises, such as riding a stationary bicycle, as the team moves forward into their exhibition schedule. Because of the nature of the strain, Abreu is unable to swing a bat or throw.
"They're the ones who are going to tell me when to start throwing and running," Abreu said. "Right now, I'll just get treatment, get better and get ready."
In Abreu's absence, 22-year-old outfielder Melky Cabrera is expected to receive additional plate appearances.
Cabrera took Abreu's place for honorary manager Yogi Berra's team in Tuesday's intrasquad game, starting in right field against a roster led by Reggie Jackson.
Yankees general manager Brian Cashman has said that a number of additional players, like Kevin Thompson and Kevin Reese, will also see additional innings in the outfield.
The Yankees open their exhibition schedule on Thursday against the Twins.
Bryan Hoch is a reporter for MLB.com. Contributor Chris Girandola added to this story. This story was not subject to the approval of Major League Baseball or its clubs.