The team has an off-day Thursday, and Rodriguez said he is fully expecting to be ready for Friday's game in Atlanta.
With one out in the fourth inning, Rodriguez motioned to the dugout, and manager Jim Leyland and a trainer visited him. Rodriguez then left the game.
"It just happened," he said. "I was squatting to catch and felt the pain."
He said that in future games he will drink lots of water to prevent something similar from happening again. Wednesday's game was played on a sunny 85-degree day in Washington.
Backup catcher Mike Rabelo entered the game in Rodriguez's place. Two batters later, a wild pitch from Detroit pitcher Jeremy Bonderman scored a run. Jason Grilli also threw a wild pitch later in the game.
Before leaving, Rodriguez grounded out in two plate appearances. Rabelo walked once and grounded out once.
Rodriguez took Tuesday off because he wanted to play Sunday in Philadelphia instead, where the stadium is much smaller than in Washington.
Michael Phillips is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.