The society had been due to perform at the town’s Webster Memorial Theatre between February 1 and February 5.
Tickets for the production had been selling well, with and sales were approaching a near sell-out before Christmas for the Saturday matinee performance on February 5.
The group made the announcement on its Facebook page at the weekend.
The statement said: “With heavy hearts we regret to announce the postponement of our forthcoming production of ‘Shrek the Musical’.
“The combination of current restrictions on indoor events and a desire to protect the health and safety of our audiences as well as all cast and crew has meant that it is not possible to proceed with the show at this time.
“We are in the process of finalising alternative dates which will be announced as soon as possible. Any tickets purchased for the February dates will remain valid.
"Theatre staff will be in touch as soon as possible to confirm the validity of your current ticket but please bear with them at this busy time.”