The man burned for several minutes in full view of television cameras that were set up outside the courthouse, where the first-ever criminal trial of a former US president is being held.
NBC News and other US media said early on Saturday the man, aged in his 30s, had died.
NBC News quoted New York City police as saying the hospital where the man was taken had declared him dead.
Ex-US president Donald Trump allegedly falsified records to conceal hush money paid to a porn star. (AP PHOTO)
Witnesses said the man pulled pamphlets out of a backpack and threw them in the air before he doused himself with a liquid and set himself on fire.
One of those pamphlets included references to "evil billionaires" but portions that were visible to a Reuters witness did not mention Trump.
The New York Police Department said the man, who they identified as Max Azzarello of St Augustine, Florida, did not appear to be targeting Trump or others involved in the trial.
"Right now we are labelling him as sort of a conspiracy theorist, and we are going from there," Tarik Sheppard, a deputy commissioner with the Police Department, told reporters.
In an online manifesto, a man using that name said he set himself on fire and apologised to friends, witnesses and first responders.
The post warns of "an apocalyptic fascist coup" and criticises cryptocurrency and US politicians, but does not single out Trump in particular.
A smell of smoke lingered in the plaza shortly after the incident, according to a Reuters witness, and a police officer sprayed a fire extinguisher on the ground.
A smouldering backpack and a gas can were visible.
Donald Trump will not be barred from office, even if he is found guilty of paying off a porn star. (EPA PHOTO)
The shocking development came shortly after jury selection for the trial was completed, clearing the way for prosecutors and defence lawyers to make opening statements on Monday in a case stemming from hush money paid to a porn star.
The court adjourned later in the afternoon.
The 12 jurors, along with six alternates, will consider evidence in a first-ever trial to determine whether a former US president is guilty of breaking the law.
Prosecutors intend to call at least 20 witnesses, according to Trump defence lawyer Susan Necheles.
Trump might testify, in a risky move that would open him up to cross-examination.
The jury consists of seven men and five women, mostly employed in white-collar professions: two corporate lawyers, a software engineer, a speech therapist and an English teacher.
Most are not native New Yorkers, hailing from across the US and countries such as Ireland and Lebanon.
The alternates, who will also hear the case, are held in reserve in case one of the jurors has to leave due to illness or some other cause.
Trump is accused of covering up a $US130,000 ($A202,600) payment his then-lawyer Michael Cohen made to porn star Stormy Daniels before the 2016 election to keep quiet about a sexual encounter she says they had a decade earlier.
Trump has pleaded not guilty to 34 counts of falsifying business records brought by Manhattan District Attorney Alvin Bragg and denies any such encounter with Daniels, whose real name is Stephanie Clifford.
Trump has pleaded not guilty in three other criminal cases as well, but this is the only one certain to go to trial ahead of the November 5 election, when the Republican politician aims to again take on Democratic President Joe Biden.
A conviction would not bar him from office.
