Technical problems at the box office for Oakengates Theatre meant tickets were double booked.
It meant people who thought they had paid £16 to see the 8 out of 10 Cats funnyman had actually bought worthless tickets.
Bosses acted today to resolve the situation after Carr agreed to put on another performance.
The 41-year-old will perform a second gig on the same night, taking to the stage at 10.30pm as well as 8pm on March 8.
The announcement comes after the theatre's booking system crashed yesterday because of the huge demand for tickets.
Many fans purchased tickets but did not receive confirmation.
The theatre's Twitter stream was flooded with concerned customers who did not know whether or not they had secured a seat in the 600-capacity theatre.
People affected will be contacted in the next two days to be offered the first chance to buy tickets for the late show before they go on general sale at 10am on January 31.
Theatre manager Debbie King said: "Because of the problems with the theatre's booking system yesterday, some payments were approved without seats being allocated.
"We apologise for this unforeseen technical issue which was beyond the control of Telford & Wrekin Council.
"However, due to the announcement of the extra show, everybody who booked a ticket before sales were suspended at 11am yesterday will now be allocated a ticket for one of the shows.
"We would ask that people bear with us while we allocate seats and we will be in contact with customers over the next 48 hours."
The show will be a warm-up for Jimmy Carr's national arena tour. He will test his new material on the audience before taking it across the UK.
Mrs King said Carr's additional show was "testimony to his popularity within Telford and his continued support for the success of local venues".
She added: "The high demand for tickets means that this second show should come as a welcome addition for customers who may not have managed to get tickets for his early evening show."
Jimmy Carr, who is best known for his deadpan delivery and dark humour, was not available for comment today. He also performed in Telford in 2012.
Anyone with queries about existing ticket bookings should contact the Box Office on 01952 382382 or visit in person.