Manager Clint Hurdle said the condition is not life threatening and Cook is being treated with blood thinners.
Cook left in the third inning of Saturday's 9-5 win against the Reds because he felt lightheaded and dizzy. The game-time temperature was 78 degrees and the day was unusually humid.
Cook, 25, was taken to Rose Medical Center for tests and remained in the hospital Sunday while doctors try to find the cause.
Cook had a complete-game victory against Arizona on Aug.1 and compiled a 6-4 record with a 4.28 ERA in 16 starts this year.