Upton, who missed the first 13 games of the season with lower back soreness, was 0-for-2 in the game.
"He just got a little bit of a cramping issue, some tightness, but it's nothing serious, it really is not," Rays manager Joe Maddon said.
Echoing his manager, Upton told reporters after the game: "No big deal."
Upton's departure set into motion a radical change of positions in the field for the Rays.
Desmond Jennings shifted from left field to center, Matt Joyce went from right to left and Ben Zobrist moved from second base to right field.
Elliot Johnson entered the game to play shortstop and hit in Upton's slot in the lineup. Sean Rodriguez moved from shortstop to third base and Will Rhymes shifted from third base to second.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.