Harry and Meghan, whose mother is African American, revealed they had named their new arrival Archie Harrison Mountbatten-Windsor on Wednesday afternoon.
Shortly afterwards, the DJ and broadcaster tweeted about the birth, and included a black and white photo showing a well-dressed man and woman holding hands with a suited chimpanzee, which he captioned: ”Royal baby leaves hospital”.
The broadcaster’s tweet was was immediately met with a backlash, with many branding it racist.
Following the negative reaction online, Baker deleted the post and apologised.
He said: “Sorry my gag pic of the little fella in the posh outfit has whipped some up. Never occurred to me because, well, mind not diseased.
“Soon as those good enough to point out it’s possible connotations got in touch, down it came. And that’s it.”
The 61-year-old, who presents a weekly show on BBC Radio 5 Live, then issued a second apology, insisting his “joke” was intended to poke fun at the Royal family.
He said: “Once again. Sincere apologies for the stupid unthinking gag pic earlier. Was supposed to be joke about Royals vs circus animals in posh clothes but interpreted as about monkeys & race, so rightly deleted.
“Royal watching not my forte. Also, guessing it was my turn in the barrel.”
The appearance of Meghan Markle’s mother, Doria Ragland, in the official royal photo of her daughter’s new-born son has been hailed as symbolic of multicultural Britain.
In the picture shared to announce the royal baby’s name, Doria and the Queen can be seen smiling adoringly down at Archie Harrison, held by a beaming Duchess of Sussex.
The Duke of Edinburgh also beamed happily at his great grandson in the snap, who is seventh in line to the throne and their eighth great-grandchild.