Witnesses say Salman Rushdie was stabbed multiple times
He was attacked on stage, and is now on a ventilator and unable to speak, Andrew Wylie said in a statement, adding that the author may lose one eye.
Mr Rushdie has suffered years of Islamist death threats after writing The Satanic Verses, published in 1988.
Police detained a suspect named as Hadi Matar, 24, from Fairview, New Jersey.
New York State Police said the suspect ran onto the stage and attacked Mr Rushdie and an interviewer at the Chautauqua Institution in western New York state.
"Salman will likely lose one eye; the nerves in his arm were severed; and his liver was stabbed and damaged," his agent, Andrew Wylie said.
No motive or charges have yet been confirmed by police, who are in the process of obtaining search warrants to examine a backpack and electronic devices found at the centre.
Mr Rushdie was stabbed at least once in the neck and in the abdomen, authorities said. He was taken to a hospital in Erie, Pennsylvania, by helicopter.
The interviewer who was with him on stage, Henry Reese, suffered a minor head injury and was taken to a local hospital. Mr Reese is the co-founder of a non-profit that provides sanctuary to writers exiled under threat of persecution.
Police told a press conference that staff and audience members had rushed the attacker and took him to the ground, and he was then arrested.
Linda Abrams, an onlooker from the city of Buffalo, told The New York Times that the assailant kept trying to attack Mr Rushdie after he was restrained.
"It took like five men to pull him away and he was still stabbing," Ms Abrams said. "He was just furious, furious. Like intensely strong and just fast."
Another onlooker, Rita Landman, told the paper that Mr Rushdie appeared to be alive immediately after the attack.
"People were saying, 'He has a pulse, he has a pulse, he has a pulse'," she said.
A video posted online shows the moment people rushed onto the stage to restrain the attacker and help the injured men. Police said a doctor in the audience gave Mr Rushdie first aid.
Indian-born novelist Mr 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, published in 1988 - The Satanic Verses - forced him into hiding for nearly ten years.
The surrealist, post-modern novel sparked outrage among some Muslims, who considered its content to be blasphemous, and was banned in some countries.
Several people were killed in anti-Rushdie riots in India and in Iran the British embassy in the capital, Tehran, was stoned.
In 1991 a Japanese translator of the book was stabbed to death, while a few months later, an Italian translator was also stabbed and the book's Norwegian publisher, William Nygaard, was shot - but both survived.
Reacting to Friday's attack, Mr Nygaard said Mr Rushdie is a "leading author who has meant so much to literature" who has paid "a high price" for his work.
A year after the book's release, Iran's Supreme Leader Ayatollah Khomeini called for Mr Rushdie's execution. He offered a $3m (£2.5m) reward in a fatwa - a legal decree issued by an Islamic religious leader.
The bounty over Mr 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 Mr Rushdie was knighted in 2007 by the Queen, it sparked protests in Iran and Pakistan, where one cabinet minister said the honour "justifies suicide attacks".
Several literary events attended by Mr 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.
UK Prime Minister Boris Johnson tweeted: "Appalled that Sir Salman Rushdie has been stabbed while exercising a right we should never cease to defend."
French President Emmanuel Macron wrote that Mr Rushdie "embodied freedom and the fight against obscurantism" and was the victim "of a cowardly attack by the forces of hatred and barbarism".
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.
In a statement, Mr Rushdie's publishers at Penguin Random House said: "We condemn this violent public assault, and our thoughts are with Salman and his family at this distressing time."
Fellow author Taslima Nasreen, who was forced to flee her home in Bangladesh after a court said her novel Lajja offended Muslim's religious faith, said she now feared for her own safety in the wake of Mr Rushdie's attack.
-- Courtesy of BBC News