Trump tweeted that Scarborough was "psycho" and "low I.Q. Crazy" Brzezinski was "bleeding badly from a face-lift" at one point.
Republican Sens. Lindsey Graham, R-S.C., and Ben Sasse, R-Neb., both frequent Trump critics, assailed the president on Twitter.
"Mr. President, your tweet was beneath the office and represents what is wrong with American politics, not the greatness of America," Graham wrote in a post.
"Please just stop. This isn't normal and it's beneath the dignity of your office," Sasse wrote.
House Speaker Paul Ryan, R-Wisc., commented on the tweets during his weekly news conference, saying that politicians are trying to "improve the tone and civility of the debate.... this obviously doesn't help do that."
Jeb Bush, the former governor of Florida and Republican presidential candidate, posted a tweet about it this afternoon, writing: "Inapropriate. Undignified. Unpresidential."
Evan McMullin, who ran as an independent candidate against Trump, sent a message to any Republicans standing with Trump, writing: "It must be said: if you're a Republican leader and you're still supporting President Trump, you own this."
"I do not think making fun of a woman's looks is acceptable. I get it every day of my life. I think that tweet is cruel - and unpresidential," McCain wrote.
She wrote in another tweet, "What does Ivanka think of this?"
The communications team for MSNBC didn't hold back in its response.
"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," the channel tweeted.
The White House is defending Trump's tweets. Deputy press secretary Sarah Huckabee Sanders told Fox News that the president has been subject to "outrageous" personal attacks on "Morning Joe."
"This is a president who fights fire with fire and certainly will not be allowed to be bullied by the liberal media and the liberal elites within the media or in Hollywood or anywhere else," she said.