The BBC's executive complaints unit upheld a complaint Ms Munchetty had made "biased comments about Donald Trump" during a segment that aired on 17 July.
The presenter gave an unscripted personal response after Mr Trump told four congresswoman of colour to "go home" on Twitter, revealing she had faced similar comments herself.
She had said: "Every time I have been told, as a woman of colour, to go back to where I came from, that was embedded in racism.
"Now, I’m not accusing anyone of anything here, but you know what certain phrases mean."
Ms Munchetty added: "[I am] furious, absolutely furious, and I can imagine that lots of people in this country will be feeling absolutely furious that a man in that position feels it's OK to skirt the lines by using language like that."
The BBC said the comments breached its guidelines, which state that presenters must "hold power to account with consistency and due impartiality."
A statement from the BBC said: "The [complaints unit] ruled that 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, overall her comments went beyond what the guidelines allow for.”
Ms Munchetty is yet to comment on the decision.
However, she has attracted support from colleagues and anti-racism campaigners.
Radio 4 Front Row presenter John Wilson questioned the decision, tweeting: "Bizarre ruling by BBC in response to 'a complaint'. One? Hope @BBCNaga is not all alone on the W1A naughty step given that the clip was tweeted out as a programme highlight."
Labour MP David Lammy wrote: "Appalling. If the BBC won't let its journalists call blatant, unashamed racism what it is, it is complicit in that racism."
Weyman Bennett of Stand Up To Racism told i: "It's appalling that Naga Munchetty has been criticised by the BBC for voicing what millions feel about the racist that is the US president.
"Stand Up To Racism stands with Naga. She was right to point to the racism that lay behind Trump's 'Go back home' comments directed at Democratic congresswomen. Trump has a history of making racist statements and untruths. This needs challenging.
"It's critical that the media are able to hold politicians to account and this transcends 'impartiality'."
He added: "We need more journalists who speak truth to power and they should be backed by senior management."
The remarks that sparked the row had targeted Democratic congresswoman Ilhan Omar, Alexandria Ocasio-Cortez, Rashida Tlaib and Ayanna Pressley. They are all US citizens and three of them were born in the US.
Mr Trump had tweeted: "So interesting to see 'progressive' Democrat congresswomen, who originally came from countries whose governments are a complete and total catastrophe, the worst, most corrupt and inept anywhere in the world (if they even have a functioning government at all), now loudly and viciously telling the people of the United States, the greatest and most powerful nation on earth, how our government is to be run.
"Why don't they go back and help fix the totally broken and crime-infested places from which they came. Then come back and show us how it is done."
He faced strong criticism for the remarks, but later insisted: "Those Tweets were NOT Racist. I don’t have a Racist bone in my body!"