Manager Robin Ventura says it is possible Cooper, who also missed Sunday's game before he knew he had vertigo, might miss a few more days.
Ventura says Cooper is ''not feeling too good.''
Bullpen coach Bobby Thigpen filled in for Cooper on Sunday and was expected to do the same Monday.
Cooper, 58, has been the White Sox's pitching coach since July 2002. He also missed 13 games over two separate stints last year with diverticulitis.