Mr Trump called Mika Brzezinski "low IQ crazy Mika", in response to disparaging remarks about him on an MSNBC show.
He also referred to her "bleeding badly from a facelift" and assailed her co-presenter Joe Scarborough.
Senator Lindsey Graham said Mr Trump's remarks were "beneath the office" of president.
He said the tweet "represents what is wrong with American politics, not the greatness of America".
"Please just stop. This isn't normal," tweeted fellow Republican Senator Ben Sasse.
Republican House Speaker Paul Ryan also joined the criticism, saying: "I don't see that as an appropriate comment. What we're trying to do around here is improve the tone, the civility of the debate. This obviously doesn't help."
MSNBC said it was "a sad day for America when the president spends his time bullying, lying and spewing petty personal attacks instead of doing his job".
But the White House sprang to Mr Trump's defence.
"I don't think that the president has ever been someone that gets attacked and doesn't push back," spokeswoman Sarah Huckabee Sanders told Fox News.
"People on that [MSNBC] show have personally attacked him many times. This is a president who fights fire with fire and certainly will not be allowed to be bullied by liberal media and the liberal elites within the media, or Hollywood or anywhere else."
Brzezinski and Scarborough co-present the MSNBC breakfast show, Morning Joe, which has increasingly derided President Trump since he took office.
In recent weeks, Scarborough has called him a "bumbling dope", resembling "a kid who pooped in his pants", while Brzezinski has mocked members of the administration as "lobotomised".
"I heard poorly rated @Morning_Joe speaks badly of me (don't watch anymore)," Mr Trump tweeted on Thursday morning.
He accused "low I.Q. Crazy Mika" and "Psycho Joe" of "insisting on joining me" at his Mar-a-Lago Florida golf resort over three days at New Year's Eve.
"She was bleeding badly from a face-lift. I said no!" he added.
The senior Democrat in the House of Representatives, Nancy Pelosi, called Mr Trump's tweets "sexist, an assault on the freedom of the press & an insult to all women".
Brzezinski is the daughter of the late Zbigniew Brzezinski, who was an aide to presidents Carter and Johnson, while Scarborough is a former Republican congressman. The couple are engaged to each other.

The 27-year-old was getting off the Southeastern train at West Wickham, Bromley, when the doors shut on her.
The driver did not see the woman on CCTV and moved off, dragging her along. She then fell under the train.
Southeastern said it had offered support to the woman after the "terrible incident" in April 2015.
The report was carried out by the Rail Accident Investigation Branch (RAIB).
A Southeastern spokesman said the company had offered to help the woman "as much as possible since the accident".
Read more on this story and others from London
The woman had tried to free the stuck bag strap but she was pulled along when the train moved and fell underneath it, resulting in "life-changing injuries", the report said.
Investigators found she was able to open the doors two seconds after the driver had begun the door closure procedure, but was given no indication that they were about to shut.
The RAIB recommended all operators who have trains which use power operated doors should make modifications to ensure passengers always had a safe amount of time to use them.
They also said drivers should watch train doors while they are closing, as well as checking all doors are shut correctly.
Neither the driver, who was a trainee, or their supervisor saw the woman on platform monitors and only found out about the accident later.
Southeastern said it had "worked very closely" with the RAIB and has "complied with all the recommendations and learning points they have made".
A spokesman said this included altering the doors on Southeastern trains to ensure they always remain open for a safe period of time.
Senior US Republicans have joined condemnation of President Donald Trump over an attack he made on Twitter against a prominent female journalist.
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A woman was seriously injured when her bag got caught in a train door, dragging her along the platform and on to the track, a report has revealed.