The Booker Prize winner, 75, was speaking at an event at the Chautauqua Institution at the time.
New York State Police said a male suspect ran up onto the stage and attacked Rushdie and an interviewer.
At a media conference, police confirmed the attacker was Hadi Matar, 24, of New Jersey.
Matar stabbed Rushdie at least once in the neck and once in the abdomen, police said.
Police said they had not yet established a motive for the attack and were still working to determine what charges would be laid against Matar. Police assumed he was acting alone and were working to confirm that.
Rushdie was initially given medical treatment by a doctor who was in the audience at the Chautauqua Institution, then airlifted to a local trauma centre where he had surgery, police said.
Police are still working to determine the charges against the suspect.
The interviewer of the event, who was also attacked by Matar, was taken to hospital and treated for facial injury, police said.
In a statement Rushdie’s agent Andrew Wylie said Rushdie was on a ventilator and would likely lose an eye after the incident.
He also suffered severed nerves in an arm and damage to his liver after being stabbed, Wylie said.
“The news is not good. Salman will likely lose one eye; the nerves in his arm were severed; and his liver was stabbed and damaged,” Wylie said in a written statement.
Witnesses told US media he was stabbed multiple times in the neck and torso area, and appeared to fall backwards as he tried to move away from the assailant.
New York Governor Kathy Hochul told a press conference about an hour later that Rushdie was alive.
He was taken to a hospital in Erie, Pennsylvania, by helicopter. There has been no further official confirmation on the extent of his injuries.
The interviewer who was also on stage, Henry Reese, suffered a minor head injury. Reese is the co-founder of a non-profit that provides sanctuary to writers exiled under threat of persecution.
The suspect was immediately taken into custody, police said.
Mark Sommer, a reporter for Buffalo News, told the BBC News Channel that the attacker had emerged from the audience in a black mask.
A video posted online shows attendees rushing onto the stage immediately following the incident.
Indian-born novelist Rushdie catapulted to fame with Midnight’s Children in 1981, which went on to sell over one million copies in the UK alone.
But his fourth book, in 1988 – The Satanic Verses – forced him into hiding for nine years.
The surrealist, post-modern novel sparked outrage among some Muslims, who considered its content to be blasphemous, and was banned in some countries.
A year after the book’s release, Iran’s Supreme Leader Ayatollah Khomeini called for Rushdie’s execution. He offered a $3 million reward in a fatwa – a legal decree issued by an Islamic religious leader.
The bounty over Rushdie’s head remains active, and although Iran’s government has distanced itself from Khomeini’s decree, a quasi-official Iranian religious foundation added a further $500,000 to the reward in 2012.
The British-American citizen – who was born to non-practising Muslims and is an atheist himself – has become a vocal advocate for freedom of expression, defending his work on several occasions.
When Rushdie was knighted in 2007 by Queen Elizabeth II, it sparked protests in Iran and Pakistan, where one cabinet minister said the honour “justifies suicide attacks”.
Several literary events attended by Rushdie have been subject to threats and boycotts – but he continues to write. His next novel, Victory City, is due to be published in February 2023.
His appearance at the Chautauqua Institution event, in western New York, was the first in a summertime lecture series hosted by the non-profit organisation.
UK Prime Minister Boris Johnson tweeted: “Appalled that Sir Salman Rushdie has been stabbed while exercising a right we should never cease to defend.”
Writer and graphic novel creator Neil Gaiman said he was “shocked and distressed” by the attack on his friend and fellow writer.
“He’s a good man and a brilliant one and I hope he’s okay,” Gaiman wrote on Twitter.
New York Governor Kathy Hochul vowed to “assist however needed in the investigation” into the stabbing.
“Here’s an individual who has spent decades speaking truth to power. Someone who’s been out there, unafraid, despite the threats that have followed him his entire adult life,” she said.
– BBC / Reuters