Ms. Munchetty’s critical remarks were shared by hundreds of thousands of people on social media, including official BBC accounts, until the company received a single complaint from a viewer. The issue was referred to the BBC’s Executive Complaints Unit, which declared on Wednesday that Ms. Munchetty’s conduct had broken its impartiality rules.

The unit said its editorial guidelines “do not allow for journalists to give their opinions about the individual making the remarks or their motives for doing so — in this case President Trump.”

“While Ms. Munchetty was entitled to give a personal response to the phrase ‘go back to your own country,’ as it was rooted in her own experience, over all her comments went beyond what the guidelines allow for,” a spokeswoman for the BBC said.

Ms. Munchetty could not be reached for comment.

Critics pounced on the Executive Complaints Unit, saying it had put too much weight on one viewer complaint while ignoring the broad impact of Mr. Trump’s comments.

“When you think about what those (mostly) older white men have got away with saying on the BBC and Twitter day after day this is a quite perplexing finding,” a Channel 4 anchor, Krishnan Guru-Murthy, wrote in a Twitter post.

Piers Morgan, who hosts a rival show on ITV and considers himself a friend of Mr. Trump, also took to Twitter to criticize the decision.