judgement" over his tweet about the Duke and Duchess of Sussex's baby.
The tweet, which he later deleted but which has been circulated on social media, showed an image of a couple holding hands with a chimpanzee dressed in clothes with the caption: "Royal Baby leaves hospital".
The BBC 5 Live presenter was accused of mocking the duchess's racial heritage.
Baker claimed it was a "stupid gag".
The 61-year-old presented a Saturday morning show on the network.
The corporation said Baker's tweet "goes against the values we as a station aim to embody".
It added: "Danny's a brilliant broadcaster but will no longer be presenting a weekly show with us."
His comment about red sauce references the Sausage Sandwich Game from his 5 Live show, in which listeners choose what type of sauce a celebrity would choose to eat.
After tweeting an apology, in which he called the tweet a "stupid unthinking gag pic", Baker said the BBC's decision "was a masterclass of pompous faux-gravity".
"[It] 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."