Cameron was due to make the trip on February 18 and 19 although it had not officially been announced for security reasons.
At a press conference about the floods that have affected huge swathes of southern England, the prime minister said he would continue to take personal command of the crisis.
"I will continue to lead the national response by chairing meetings of the government's emergency committee, Cobra. I'm cancelling my visit to the Middle East next week," he told reporters.
It would have been Cameron's first visit to Israel since he was elected in 2010, although the Conservative leader did visit while he was in opposition.