The decision was taken because of the forecast of severe weather due to Storm Barra, including very strong winds.
The outdoor event, which is sold out, takes place in the woods on the Sewerby estate, and the forecast means it would be potentially unsafe to hold the events.
Ticket holders are being contacted directly via email, which will explain the options available.
Marie Gascoigne, general manager at Sewerby Hall and Gardens, said: “We are very sorry indeed to have to cancel the performances on Tuesday, but of course the safety of our visitors, staff and the actors taking part has to come first.
“Customers affected should keep an eye open for their all important email.”