The tweet from Danny Baker, a host on BBC radio station 5 Live and a well-known British media figure, showed an image of a couple holding hands with a chimpanzee dressed in clothes and a bowler hat, alongside the caption, "Royal Baby leaves hospital." The tweet has since been deleted.
He was accused of making fun of Markle's African American heritage. According to The Hollywood Reporter, a BBC representative said it was a "serious error of judgment" and that Baker would "no longer be presenting a weekly show with us."
The corporation added that Baker's tweet "goes 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."
Baker, 61, who presented a weekend show on the network, initially apologized for the tweet. "Sorry my gag pic of the little fella in a posh outfit has whipped some up," he wrote. "Never occurred to me because, well, mind not diseased. Soon as those good enough to point out its possible connotations got in touch, down it came. And that's it."
Later on, he wrote that he would have used the "same stupid pic for any other Royal birth or Boris Johnson kid or even one of my own. It's a funny image. (Though not of course in that context.) Enormous mistake, for sure. Grotesque."
Baker tweeted about BBC's decision to fire him, saying that "the call to fire me... was a masterclass of pompous faux-gravity."
"Took a tone that said I actually meant that ridiculous tweet and the BBC must uphold blah blah blah," he added. "Literally threw me under the bus. Could hear the suits' knees knocking."
Baker told reporters outside his home, "I do not, not understand all of this. I get it. But for 5 Live to chuck us under the bus like this, dear Lord."
Through his work on his Saturday morning show on BBC 5 Live, Baker won a Sony Gold Award for Speech Radio Personality of the Year in 2011, 2012 and 2014 and a Gold Award for Entertainment Show of the Year in 2013, according to the BBC.
This week's firing marks the second time he was terminated by 5 Live and the third time he left the BBC. In 1997, he was reportedly fired for encouraging soccer fans to make a referee's life hell after the official awarded a controversial penalty in an FA Cup tie.
In 2012, weeks before he was inducted into the Radio Hall of Fame, he made headlines for an on-air rant in which he resigned and branded his bosses at BBC London "pinheaded weasels" after they asked him to move from a weekday show to a weekend.