The Build-A-Bear toy chain advised customers against planning trips to its stores on Thursday after a "Pay Your Age" event led to "extreme crowds and safety concerns".
The retailer said there had been an "unprecedented" response to the promotion in which customers pay the age of the child they are accompanying for one of a range of stuffed toys, which normally cost around £20.
In a statement, Build-A-Bear said: "The response to our Pay Your Age Day event at all of our UK locations has been overwhelming and unprecedented in our 21-year history.
"The crowds have greatly exceeded our expectations and, per local authorities, queues are at capacity and we cannot accept additional guests due to extreme crowds and safety concerns.
"We understand our guests are disappointed, and we are working to address the situation. We will reach out directly to our valued guests as soon as possible."
Customers who attempted to take advantage of the offer took to social media to report staff advising them that they could have to queue for hours.
Build-A-Bear warned on Wednesday that it was anticipating long lines and waiting times, adding that it would "make every effort to help as many guests as possible participate in this first-time event".
The HotUKDeals website posted on Facebook this morning: "Uh oh ... Build a Bear pay your age event is drawing INSANE crowds.
"People are being told NOT to go as at least three store have been forced to closed due to sheer numbers of people turning up and worries for peoples safety!"