The BBC Radio 5 Live host sparked outrage after he uploaded an image of a couple holding hands with the animal, with the caption: 'Royal baby leaves hospital.'
He later removed the picture after he was hit by a huge backlash with users branding it 'racist' because of Meghan's heritage.
Baker posted the image just hours after Prince Harry and Meghan showed off baby Archie to the world at Windsor Castle yesterday.
This morning the broadcaster said he had been 'fired' in a post on Twitter as the outrage continued to mount.
He wrote: 'Just got fired from @bbcradio5live. It was red sauce, always.'
The BBC confirmed his tweet, and said in a statement: 'This was a serious error of judgment and goes against the values we as a station aim to embody.
It was obviously a mistake.
‘I have made a full apology. Yes of course I’ve made a full apology.
‘I put up silly pictures all the time. But that’s all. I think even you must realise that it was a mistake.
‘I’m shocked at my own foolishness.’
After he removed the image following the huge backlash against him, Baker wrote: '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.
'Now stand by for sweary football tweets.'
Twitter users called on the BBC to sack him following the tweet, which came just hours after Prince Harry and Meghan revealed baby Archie to the world.
One wrote: 'Danny Baker posts an image comparing Archie - a Royal newborn with African heritage, to an APE.
'Danny Baker should be sacked this morning!!!'
Another wrote: 'RACIST RACIST RACIST Danny Baker should be given today to resign and clear his desk.
'If he is still there at 16.59 @bbc MUST FIRE HIM! I'm disgusted by the hate and racism inherent in his Tweet Unforgivable HE's not fit to be a broadcaster employed from the public purse.
Another said: 'Wow that didn't take long.
'Royal Baby is just two days old and he's already being trolled by Danny Baker who has compared him to a chimpanzee...and Baker claims he's not racist.'