Speaking to the BBC's Newscast, Murdoch said the closures could see more than 1,600 jobs lost.
He added that the Government schemes provided to help the restaurant industry do not do enough to overcome the combination of fixed costs and lost sales.
"I don't think you can ever get over the top of this problem," he said.
Discussing the 'Eat Out to Help Out' scheme announced yesterday by Chancellor Rishi Sunak, which will provide a 50% reduction (up to a value of £10 per head) for sit-down meals in cafes, restaurants and pubs across the UK between Monday and Wednesday every week throughout August, Murdoch said he expected Burger King to participate and described it as an "innovative approach".
However, despite that scheme and other Government support, he said the chain could be pushed to close a number of its UK locations as a result of paying rent while "taking absolutely no money".
Such closures would lead to the loss of between 800 to 1,600 jobs from the group's 16,500-strong workforce.
"If we can possibly avoid it, we will," he said.
"We don't want to lose any. We try very hard not to, but one's got to assume somewhere between 5% and 10% of the restaurants might not be able to survive.
“It’s not just us - I think this applies to everyone out there in our industry.
"Some of these high streets - they’re not coming back.”