"It could lead to a weapons program inside of Iran that could lead other states in the region to embark on their own programs," Brennan said in an interview with the BBC aired on Wednesday.
"So I think it would be the height of folly if the next administration were to tear up that agreement."
Brennan also said that in dealing with the Syrian crisis, Trump should be cautious in trying to work with Russia.
"I hope there is going to be an improvement in relations between Washington and Moscow," he said.
"President-elect Trump and the new administration need to be wary of Russian promises. Russian promises in my mind have not given us what it is that they have pledged."