Slater was taken ill Friday while rehearsing in London, the BBC reported. Producers, however, remain hopeful Slater will recover in time to appear in the first performance Aug. 6.
Slater, star of True Romance and Robin Hood: Prince of Thieves, plays Randle P. McMurphy in the production, a role made famous by Jack Nicholson in the Oscar-winning 1975 film.
The play, written by Dale Wasserman, is adapted from the book by the late Ken Kesey.
2014: The Year in Music [PHOTOS]