"I think it would be the height of folly if the next administration were to tear up that agreement," Brennan told the BBC.
He said it would be "almost unprecedented" for one administration to tear up an agreement made by a previous one.
Brennan warned "it could lead to a weapons programme inside Iran that could lead other states in the region to embark on their own programmes, with military conflict".
Since his election, Trump has been more circumspect, not publicly discussing the international deal with Tehran aimed at preventing the Islamic republic from developing nuclear weapons.
But his pick to succeed Brennan as head of the Central Intelligence Agency (CIA), Mike Pompeo, is a strident critic of the agreement.
In the BBC interview, Brennan also expressed hope there would be an improvement in relations between Washington and Moscow.
But he warned: "I think 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 they had pledged."
Trump had said he might authorise the torture of detainees, including waterboarding, to gain information, but has since said he had received advice that made him rethink his approach.
"I would counsel my successor not to go down that road any more," Brennan said.