Hadi Matar, 24, has appeared in court and has been remanded without bail, the prosecutor said.
Matar ran onto the stage and attacked Mr Rushdie and an interviewer at the event in western New York state.
The award-winning writer is in a critical condition.
Mr Rushdie, 75, has faced years of death threats for his novel The Satanic Verses, which some Muslims see as blasphemous.
“This is the very early stage of what will invariably be a protracted legal process,” District Attorney Jason Schmidt said in a statement.
There has been an outpouring of support, with the attack condemned as an assault on freedom of expression.
The writer has been put on a ventilator, is unable to speak, and may lose one eye, his agent said.
Mr Rushdie was stabbed at least once in the neck and in the abdomen, authorities said. He has sustained liver damage, too.
The interviewer who was with Mr Rushdie, Henry Reese, suffered a minor head injury and was taken to a local hospital. Mr Reese is the co-founder of a non-profit organisation that provides sanctuary to writers exiled under threat of persecution.
No motive or charges have yet been confirmed by police, who have said they want to examine a backpack and electronic devices found at the centre.
Watch: Video shows the moments after author Salman Rushdie was attacked