The president, an avid cable news watcher, appears to have been responding to sharp comments by Brzezinski.
"I heard poorly rated @Morning_Joe speaks badly of me (don't watch anymore)," Trump wrote, referring to a morning news show featuring Brzezinski and co-host Joe Scarborough.
"Then how come low I.Q. Crazy Mika, along with Psycho Joe, came to Mar-a-Lago 3 nights in a row around New Year's Eve, and insisted on joining me. She was bleeding badly from a face-lift. I said no!" Trump tweeted.
The president, an avid cable news watcher, appears to have been responding to sharp comments by Brzezinski during Thursday "Morning Joe" program on the left-leaning MSNBC cable network.
"Everybody in Washington," Brzezinski said, "in the administration, needs to look at this from... a point of view where they're not lobotomized because you're sitting in there and you're so scared of him, and you think you need to suck up to the president."
If a boss at NBC -- MSNBC's parent company -- "started tweeting wildly about people's appearances, bullying people, talking about people in the competition, lying every day, undermining his managers, throwing them under the (bus) -- that person would be thrown out.
"It's just not normal behavior," she said. "In fact, there would be concerns that the person who runs the company is out of his mind."
Brzezinski appeared to be uncowed by Trump's Twitter attack. She responded to his tweet with a post of her own, a photo of a young child reaching for Cheerios cereal.
"Made for little hands," the picture caption read -- a schoolyard taunt that has been leveled against the image-conscious Trump since the days of his candidacy.
Scarborough re-tweeted a comment from CNN reporter Jake Tapper: "This reminds me: how is @FLOTUS's campaign against cyber-bullying going?" it said, referring to First Lady Melania Trump.
Trump was often interviewed on "Morning Joe" during the 2016 presidential campaign, but as the White House relationship with much of the US media has soured he has recently favored interviews with friendly right-wing outlets.
Brzezinski, 50, is the daughter of the late Zbigniew Brzezinski, who was president Jimmy Carter's national security advisor.
Scarborough, 54, is a Republican former congressman who represented a Florida district in the 1990s.
The two are engaged to marry.