The move came shortly after Trump met Senator Rand Paul, who said earlier that he planned to ask the President to revoke Brennan's clearance.
The former Obama Administration CIA director last week used the word "treasonous" to describe Trump's performance at his summit with Russian President Vladimir Putin in Helsinki, saying it showed he was "wholly in the pocket of Putin."
In a tweet shortly after Sanders' announcement, Paul appeared to take credit for the move.
"Just got out of WH meeting with @realDonaldTrump," Paul tweeted. "I restated to him what I have said in public: John Brennan and others partisans should have their security clearances revoked."
"Public officials should not use their security clearances to leverage speaking fees or network talking head fees," he added.
Democrats immediately criticised the move as an attempt to punish former officials for levelling criticism at Trump.
"This is what totalitarianism looks like," Senator Mazie Hirono, (D), tweeted.
At least two of the officials - Comey and McCabe - do not currently have clearances.
Comey hasn't had a security clearance for many months, according to a person familiar with the matter.
McCabe's clearance was deactivated when he was fired from the FBI, said Melissa Schwartz, a spokeswoman for McCabe. She said McCabe's lawyers were told that was according to FBI policy.
"You would think the White House would check with the FBI before trying to throw shiny objects to the press corps," she wrote on Twitter.
Clapper, a career intelligence officer who last served as the Director of National Intelligence in the Obama Administration, described the move by the White House as "unprecedented" and "petty."
Clapper said there were no grounds for dismissing his clearance, and that the White House's actions were directed solely at "people who have criticised the President." He said no one from the White House has contacted him about the matter, which he learned about during Sanders' remarks.
Clapper also said he could not think of an instance in which a president revoked a security clearance.
Former CIA and NSA director Michael Hayden had no comment on the White House's statement. But he objected to any White House suggestion that he had mishandled classified information or done anything that would be grounds for revoking his security clearance.
It's routine for the former directors of intelligence agencies to maintain their security clearance after they've left the government. This lets them consult with current intelligence officials and share their expertise, current and former officials said.
Brennan and Rice did not immediately react to the news.
Former CIA directors typically hold on to their clearance for several years after leaving office in part so that they can share insights with current directors.
