In the cartoon, drawn by Sean Delonas, a regular Post cartoonist, two officers are staring gloomily at the blood spattered chimp's corpse after one of them has shot it.
"They'll have to find someone else to write the next stimulus bill," says the other officer.
The cartoon drew immediate criticism from Al Sharpton, the black activist and community leader.
In a statement, Mr Sharpton said the cartoon was "troubling at best given the historic racist attacks of African-Americans as being synonymous with monkeys".
He said that it could be asked whether the cartoonist was "making a less than casual reference to this" and could be "inferring that a monkey wrote the last bill".
David Patterson, the black governor of New York state, later joined Mr Sharpton in asking for an "explanation" from the newspaper.
Col Allan, editor-in-chief of the Post, said: "The cartoon is a clear parody of a current news event, to wit the shooting of a violent chimpanzee in Connecticut.
"It broadly mocks Washington's efforts to revive the economy.
"Again, Al Sharpton reveals himself as nothing more than a publicity opportunist."
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