In July, BBC Breakfast presenter Ms Munchetty condemned comments made by US president Donald Trump about political rivals as racist. In an inflammatory tweet, he had told female Democrats to “go back” to their own counties.
On Wednesday, Ms Munchetty was issued a formal rebuke for her remarks, provoking a fierce backlash.
It has prompted director-general Lord Tony Hall and other executives to send letters to BBC staff addressing the decision.
It assured staff “racism is racism” and that “diversity matters hugely”.
The letter states in part: “You will have heard a lot of comment over the past few days about the BBC and the reporting of racism.
“The BBC is not impartial on racism. Racism is not an opinion and it is not a matter for debate. Racism is racism.
“Naga Munchetty – one of our stars – was completely within her rights to speak about the tweets of Donald Trump which have been widely condemned as racist.”