Rushdie was treated on stage then taken to hospital by helicopter
The suspect was arrested at the scene and is in custody, New York State Police say.
Rushdie faced death threats and went into hiding for nearly a decade after his book The Satanic Verses was published in 1988.
Iran at the time issued an edict calling for his death.
Iranian state-run media outlets added $600,000 to a bounty for the killing of Salman Rushdie in 2016, Reuters news agency reported at the time.
Some $3m (£2.5m) was originally offered for his execution in 1989 by the then Supreme Leader of Iran, Ayatollah Khomeini, over the publishing Rushdie’s novel The Satanic Verses.
The book sparked outrage among some Muslims, who considered its content blasphemous, and it was banned in some countries.
On the 27th anniversary of the original edict, Iran’s Fars news agency published a list of 40 news outlets adding to the bounty – with Fars itself earmarking $30,000.
While Iran’s government has distanced itself from Khomeini’s decree, Reuters reported in 2016 that Iranian hardliners said it was irrevocable and eternal after his death. (BBC)