The Coventry Festival of Motoring, which attracted 40,000 visitors in 2014, has had ??20,000 of funding withdrawn by the city council.
However, organisers Culture Coventry said the funding withdrawal was "not the only reason" they had made the decision to cancel the event.
It said events planned for 2015 and 2016 have been axed.
Organisers said they had not ruled out reviving the festival, but it would remain on hold indefinitely.
The free heritage event, which features classic cars, was due to take place in August at Stoneleigh Park.
It is organised by Culture Coventry, a trust set up to manage four of the city's visitor attractions.
Chief executive Gary Hall said he had just found out about the council's funding withdrawal.
"I have to look at the ongoing viability of the show and with cuts coming from the city council and other sponsors, we would not be able to grow it as we have in recent years," he said.
"It is a lot of money and, as a charity running four attractions in the city, we have to look at what benefits we are getting."
He said the charity was reopening Coventry's Transport Museum in June following a ??9m redevelopment.
"Unfortunately, we have to put all of our resources into promoting the museum," he said.
Mr Hall said the charity would run "a number of events" throughout 2015 to bring classic car owners into Coventry.
Coventry MotoFest, a more recent addition to the city's festival calendar, which features car races and displays, will go ahead in May, as planned.
A motoring festival which has been running for 30 years is to be cancelled, organisers have said.