Councillor Peter Cherrington said although talks were continuing with Morrisons to find a way forward for the £45 million redevelopment of the town's Smithfield site, Cineworld had pulled out of the scheme.
The cinema had been lined up as part of the redevelopment, which was also going to include a Morrisons supermarket and number of restaurants.
Although the scheme has delivered a new state-of-the-art livestock market, the other parts of the redevelopment have stalled.
Cineworld and Morrisons have refused to publicly say whether the complete project will definitely go-ahead although the supermarket giant did last year admit it was reconsidering its options because of "uncertainties" with Cineworld.
Councillor Cherrington revealed the news during a question and answer session with the Shropshire Star's sister paper The Oswestry and Border Chronicle at Oswestry Chamber of Commerce last night.
He said a ruling made as part of the initial planning application which was granted five years ago for the supermarket was that the cinema had to be built first.
Councillor Cherrington said: "The planning application said they had to put a cinema in before anything else was built.
"But Cineworld are not going to build in Oswestry and that has left Morrisons in a very difficult position."
The mayor said Morrisons was still keen to remain involved in the project.
Councillor Cherrington said: "The town council and Shropshire Council are now in talks with Morrisons to reset the planning application so that they can go ahead."
The mayor said the £3 million in capital receipts the town council as owner of the site had already received as part of the supermarket deal would remain with the authority, no matter what happens in the future.