The injuries are reportedly proving tricky for the pair as they have to stage a physical fight scene in the play, based on the novel of the same name by Patricia Highsmith, which was turned into a thrilling 1951 movie by Alfred Hitchcock.
The show's co-producer Michael Rose tells Britain's Mail on Sunday newspaper, "Laurence got his because he had a chest infection and coughed so much that he cracked a rib. Jack... I couldn't get to the bottom of how he did that. Perhaps because of the physical exertion of the show."
A spokesperson for the show was also unable to ascertain how Huston broke his rib.