In the defamation case, Mrs Palin says the newspaper published a statement about her that it "knew to be false".
A 14 June editorial appeared to tie Mrs Palin to a 2011 shooting spree that left congresswoman Gabby Giffords seriously wounded and six others dead.
Mrs Palin is reportedly seeking more than $75,000 (£58,000) in damages.
The former Alaska governor's lawyers argue "the Times' conduct was committed knowingly, intentionally, wilfully, wantonly and maliciously, with the intent to harm Mrs Palin".
The lawsuit says the newspaper displayed "blatant disregard of the substantial likelihood of causing her harm, thereby entitling Mrs Palin to an award of punitive damages".
The legal action, filed in the United States District Court for the Southern District of New York, argues the publication "violated the law and its own policies".
The editorial, headlined "America's Lethal Politics", was published on the day a gunman opened fire on Republican congressmen as they played baseball in Alexandria, Virginia, critically injuring a Louisiana legislator.
The article said an advert from Mrs Palin's political action committee had placed "Giffords and 19 other Democrats under stylized cross hairs".
A day later, the New York Times issued a correction, noting that "no such link was established" between the Palin ad and the shooting of Gabby Giffords in Arizona.
The newspaper also conceded that the ad in question "depicted electoral districts, not individual Democratic lawmakers, beneath stylized cross hairs".
But the New York Times maintained the error did not "undercut or weaken the argument of the piece".
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Mrs Palin said the newspaper's response "did not approach the degree of the retraction and apology necessary and warranted by The Times's false assertion that Mrs Palin incited murder".
In a statement, Danielle Rhoades Ha, a spokeswoman for the New York Times, said: "We have not reviewed the claim yet but will defend against any claim vigorously."
Mrs Palin's legal team includes Kenneth Turkel and Shane Vogt, who represented Hulk Hogan as he won $115m in a lawsuit against Gawker Media Group.
In the aftermath of the 2011 shooting, Mrs Palin described suggestions that she was somehow to blame for the Giffords shooting as a "blood libel".