"We will have to see how he feels," manager Joe Girardi said.
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An MRI revealed the extent of the injury Saturday, showing no signs of a strain or tear in the hamstring.
Granderson said he initially felt something while running out to his position prior to the top of the first inning. He got through the first inning and a half, but felt something again prior to his first at-bat.
Granderson told Girardi and the training staff that he thought he could play through the injury, but they were concerned that he might further aggravate it while going hard for a ball in the field or trying to score from first base, so they elected to pull him from the game.
Granderson said the at-bat had no affect on the injury.
"It's good," Granderson said of the MRI results. "But the good thing is even prior to that I didn't feel a pop or a snap or anything like that. Something just didn't feel right. I'm day to day. Probably not as soon as tomorrow, but it could be, so that's really good news."
The team already has lost left fielder Brett Gardner for the season and is without first baseman Mark Teixeira and third baseman Alex Rodriguez.
Rodriguez, rehabbing from a broken hand in Tampa, may be back against the Rays as early as Monday. Teixeira, out with a calf strain, won't return until later this week, at the earliest.
On Saturday, manager Joe Girardi shifted Ichiro Suzuki to center to replace Granderson. Nick Swisher moved from first to right.
Granderson hasn't been much help lately. In his last 22 games, he is hitting .176 with 23 strikeouts. He entered Saturday hitting .235 with 34 homers and 79 RBIs. When he left the game, his 159 strikeouts were tied for second in all of baseball.
Information from ESPNNewYork.com special contributor Mike Mazzeo was used in this report.
Andrew Marchand is a senior writer for ESPNNewYork. He also regularly contributes to SportsCenter, Baseball Tonight, ESPNews, ESPN New York 98.7 FM and ESPN Radio. He joined ESPN in 2007 after nine years at the New York Post. Follow Andrew on Twitter »