The BBC Radio 5 Live host uploaded an image showing a well-dressed man and woman holding hands with a monkey, who was in a suit.
The snap came with the caption: “Royal baby leaves hospital.”
Danny Baker, 61, later deleted the picture and apologised on Twitter after receiving backlash.
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.”
In another tweet, he wrote: “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.”