Danny Baker, a broadcaster with BBC Radio 5 Live, had tweeted the image.
The BBC has fired a British radio presenter who tweeted an image of a chimpanzee dressed in clothes below the caption "Royal Baby leaves hospital".
Meghan, wife of Prince Harry, gave birth in the early hours of Monday morning to a baby boy, Archie, the first mixed race child to be born into a senior position in British royalty in recent history.
"Just got fired," Danny Baker, a broadcaster with BBC Radio 5 Live, said on Twitter.
The BBC said the tweet was a serious error of judgment that went "against the values we as a station aim to embody".
"Danny's a brilliant broadcaster but will no longer be presenting a weekly show with us," the BBC said.
Meghan, whose mother is African-American and father is white, has been the target of racist commentary on social media in the past.
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