Brzezinski appeared to respond to the president's tweets with an image of a Cheerios box that says "Made For Little Hands."
The White House stood by Trump's tweets Thursday. Sarah Huckabee Sanders, the president's principal deputy press secretary, said Trump "fights fire with fire."
Trump's tweets came after Scarborough harshly criticized the White House over a Politico report detailing the way Secretary of State Rex Tillerson yelled at top Trump aides for undermining him and holding up State Department appointees. Jared Kushner, the president's son-in-law and senior adviser, reportedly told another top aide after the incident it was "unprofessional."
"What Rex Tillerson did was not unprofessional," Scarborough said. "What Rex Tillerson did was patriotic and way overdue. This White House ― because Donald Trump wants his son-in-law to be the de facto secretary of state and anybody going in there knows that he wants Jared to be the de facto secretary of state, so they have cut Rex Tillerson off at the knees every single day. They don't let him put in qualified people at the State Department."
Brzezinski referred to Kushner as "the guy with no experience."
Earlier this morning, Dan Scavino, the White House's director of social media, called Brzezinski "dumb as a rock" on Twitter:
Trump's tweets also came a day after Fox News' Sean Hannity, a Trump ally, ripped Scarborough's coverage of Trump.
"It's a sad day for America when the president spends his time bullying, lying and spewing petty personal attacks instead of doing his job," MSNBC said in a statement Thursday.
Mark Kornblau, the senior vice president of NBCUniversal News Group, tweeted Thursday that he thought it would be beneath his dignity to respond to Trump's comments.
Two Republican senators, Lindsey Graham of South Carolina and Ben Sasse of Nebraska, criticized Trump's comments:
Ironically, Trump's wife, Melania, pledged to take on cyberbullying as first lady ― "especially in social media."
"Our culture has gotten too mean and too rough, especially to children and teenagers," the first lady said in a November campaign speech. "It is never OK when a 12-year-old girl or boy is mocked, bullied or attacked. ... It is absolutely unacceptable when it is done by someone with no name hiding on the internet."
Trump's Thursday morning tweets evoke his attack on Megyn Kelly in 2015, when he accused her of having "blood coming out of her wherever." The tweet also comes after the president called a female Irish reporter over to his desk in the Oval Office earlier this week to compliment her physical appearance.
Trump has a long, storied history of body-shaming and publicly humiliating women. As the owner of the Miss Universe pageant in 1996, he called Venezuelan contestant Alicia Machado "Miss Piggy" ― because he thought she'd gained weight ― and "Miss Housekeeping." He said in 2013 that celebrity Kim Kardashian had gotten "a little bit large" and shouldn't dress like she's 120 pounds. He has called comedian Rosie O'Donnell "fat" and a "slob," and he infamously mocked fellow presidential candidate Carly Fiorina's appearance. "Look at that face! Would anyone vote for that?" he told Rolling Stone in an interview during his primary campaign.
Also during his 2016 campaign, Trump was forced to apologize after The Washington Post published a 2005 tape in which he openly bragged about being able to grab women "by the pussy" because he was a celebrity. Trump dismissed the tape as "locker room talk."
Scarborough and Brzezinski are engaged and Trump reportedly offered to officiate at the couple's wedding.
This article has been updated with more reactions and background.