Rodriguez had been in New York's original Game 1 lineup batting cleanup against Rays right-hander James Shields. Rodriguez was replaced at third base by Cody Ransom and will be the designated hitter when the Yankees face right-hander Matt Garza in Game 2.
"I probably just slept on it wrong," Rodriguez said. "That's never happened to me before. It feels OK, and I'm going to give it a shot in the second game."
Rodriguez is batting .308 with 33 home runs and 95 RBIs in 126 games this year.
The defending American League MVP, Rodriguez is batting .344 (53-for-154) in his past 41 games at Yankee Stadium. He had just four hits in his last 22 at-bats on the club's 10-game, four-city road trip that concluded Wednesday.
New York dropped the opener of the twin bill to Tampa Bay, 7-1, marking the 47th time that the Yankees has scored two runs or fewer this season. They are 11-36 in those games.
"It's frustrating to not consistently be able to put up runs," Rodriguez said. "Overall, it's been a struggle, not just the offense."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.