After the president's tweets, Reddit users expressed disbelief at the president's use of the clip.
It was also retweeted by the official presidential Twitter account, @POTUS, operated by the White House.
Mr Trump has repeatedly clashed with the CNN news network, which he calls "fake news".
CNN's top White House correspondent Jim Acosta, who has been critical of the White House's attitude to the press, simply tweeted: "Isn't pro wrestling fake?"
Meanwhile, the CNN Communications team tweeted a seemingly sarcastic response quoting White House press officer Sarah Huckabee Sanders, who said on Thursday: "The President in no way form or fashion has ever promoted or encouraged violence. If anything, quite the contrary."
In a later statement, the news network said "clearly, Sarah Huckabee Sanders lied... [he is] involved in juvenile behaviour far below the dignity of this office."
"We will keep doing our jobs. He should start doing his."
The pro-wrestling president, by Anthony Zurcher, BBC News, Washington
Donald Trump has shown time and time again that he views politics as performance art; another reality television competition where the more drama and conflict there is, the better.
His CNN-wrestling video tweet is just the latest, most jarring example. For Mr Trump the political process is like a World Wrestling Entertainment match. The plot is contrived; the action is fake; the outcome predetermined.
During his campaign, he pulled back the curtain on the show and laughed along with his supporters at the spectacle. He encouraged his crowds to cheer the hero (him) and berate the villains (everyone else).
As president, nothing has changed. CNN has just been chosen as the latest number-one bad guy.
The president's tweet will certainly harshen the level of discourse in the nation. Already there are accusations that Mr Trump is inciting violence.
Most of his supporters, however, will see it as Mr Trump probably intended - the latest episode in the biggest show ever to hit the US political scene; the newest twist in the remaking of the modern US presidency.