The team said Dunn felt discomfort during Kansas City's 7-6, 12-inning victory Tuesday and was taken to a hospital after the game. He was expected to travel with the team to Chicago after a Wednesday afternoon game.
Dunn scored a run and was 0 for 4 with a walk and a hit-by-pitch against the Royals.
Dunn is hitting .286 with one home run and needs 45 homers to reach 400. The offseason acquisition signed a four-year, $56 million contract with the White Sox.