Jurassic Live – which is touring theatres and areas in the UK – had been due to take place at the Stafford Gatehouse Theatre on Saturday.
Performances had been due to start at 1pm and 5pm, but they have both been postponed until a soon-to-be-announced date due to the illness.
A statement from the theatre on Friday said: "Sorry to announce tomorrow's Jurassic Live performances have had to be postponed due to cast illness.
"Both the Gatehouse and the producers sincerely apologise for the inconvenience caused. Customers will be contacted as soon as possible with further information."