The cartoon refers to a chimpanzee named Travis who was killed Monday by police in Stamford, Conn., after it mauled a friend of its owner.
Obama signed his administration's economic stimulus plan on Tuesday.
Critics called the cartoon racist and said it trivialized a tragedy in which a woman was disfigured and a chimpanzee killed. Many urged a boycott of the Post and the companies that advertise in it.
"How could the Post let this cartoon pass as satire?" said Barbara Ciara, president of the National Association of Black Journalists. "To compare the nation's first African-American commander in chief to a dead chimpanzee is nothing short of racist drivel."
The Rev. Al Sharpton called the cartoon "troubling at best given the historic racist attacks of African-Americans as being synonymous with monkeys."
Sharpton planned to picket the Post on Thursday along with others.
Col Allan, editor-in-chief of the Post, defended the work. "The cartoon is a clear parody of a current news event, to wit the shooting of a violent chimpanzee in Connecticut," Allan said in a statement. "It broadly mocks Washington's efforts to revive the economy. Again, Al Sharpton reveals himself as nothing more than a publicity opportunist."
The cartoon drew hundreds of comments on the Internet including at the liberal Huffington Post, where columnist Sam Stein wrote: "At its most benign, the cartoon suggests that the stimulus bill was so bad, monkeys may as well have written it. Most provocatively, it compares the president to a rabid chimp."
It is not the first time that Delonas, the longtime cartoonist for the Post's Page Six, has raised eyebrows with a heavy-handed caricature.
An earlier Delonas cartoon made fun of Paul McCartney's ex-wife Heather Mills for having only one leg, and another compared gay people seeking marriage licenses to sheep lovers. In a cartoon last month, an enormous Jessica Simpson dumps boyfriend Tony Romo for Ronald McDonald.
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