Naga Munchetty breached BBC guidelines by criticising President Donald Trump for perceived racism, the corporation's complaints unit has ruled.
In July the BBC presenter took issue with comments made by the US President after he told opponents to "go back" to the "places from which they came".
The BBC said the Breakfast host was entitled to her own views but had gone "beyond what the guidelines allow for".
It said any action taken as a result of the finding would be published later.
A BBC spokeswoman said the corporation's Executive Complaints Unit [ECU] had 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".
Speaking on BBC Breakfast on 17 July after Mr Trump's online remarks, Munchetty 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."
Munchetty said she felt "absolutely furious" and suggested many people in the UK might feel the same way.
"I can imagine lots of people in this country will be feeling absolutely furious that a man in that position feels it's okay to skirt the lines with using language like that," she told co-presenter Dan Walker.
Her comments followed Mr Trump posting several messages that made references to the Democrat politicians Ilhan Omar, Alexandria Ocasio-Cortez, Ayanna Pressley and Rashida Tlaib.
"Why don't they go back and help fix the totally broken and crime infested places from which they came," he wrote on Twitter on 14 July.
Some BBC journalists tweeted their disapproval at the ECU's ruling.
Presenter Carrie Gracie, who resigned her post as China Editor in a dispute over equal pay, said it had caused "unease" among BBC journalists "for whom 'go back' = racist" and called on the ECU to explain its decision.
#nagamunchetty Unease among #BBC journalists for whom ‘go back’ = racist. If power trumps or bends meaning then no point in journalism, just print propaganda. There is no #BBC journalism worth the name without #BBC values. Accountability is one. Explain @BBCNaga reprimand please.— Carrie Gracie (@BBCCarrie) September 25, 2019
BBC correspondent Sangita Myska tweeted: "Right now, there is a lot of bewilderment among BAME [black, Asian and minority ethnic] staff", adding "there is unique self-censoring that BAMEs do across all industries & workplaces".
Replying to Ms Myska, presenter Matthew Price tweeted his "solidarity", saying: "There's a lot of bewilderment (and some anger) among non-BAME staff too... and I agree there's general concern about voicing it openly."
When Munchetty made the comment in July, she received praise online for her "off-script" moment.
The ECU found Munchetty's assertion that Mr Trump's comments were "embedded in racism" went beyond what the BBC allows and upheld a complaint made about the presenter's comments.
Channel 4 news anchor Krishnan Guru-Murthy tweeted he found the decision to partially uphold the complaint "perplexing".
"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."
The BBC's spokeswoman said a summary of the complaint and the ECU's decision would be published on the BBC's online complaints pages and that it would "include a note of any action taken as a result of the finding".
A representative for BBC Breakfast said Munchetty was not available for comment.