Chavez grabbed his side after fouling off the second pitch he saw from Texas right-hander Justin Grimm on Thursday. Chavez also fouled off the first pitch.
Cliff Pennington replaced Chavez and eventually grounded out.
The 35-year-old Chavez is hitting .325 as a part-time starter at third base.
Chavez missed much of four straight seasons from 2008 to 2011 with back, neck and shoulder problems and a broken foot. He was on the seven-day concussion disabled list with the New York Yankees last season.