Matar pled not guilty to charges of attempted murder and assault with a weapon during his court appearance.
Rushdie was stabbed roughly 10 times as he was taking the stage to deliver a lecture in what prosecutors said was a premeditated and targeted attack.
The 75-year-old writer had stab wounds to his neck and stomach, as well as puncture wounds to his right eye and chest, as well as a laceration on his right thigh, according to the district attorney.
Rushdie's agent told The New York Times that the news was not good. The nerves in his arm were severed and he may lose an eye.
Matar was carrying two fake IDs when he was arrested, according to The New York Times. After he entered his not guilty plea, he was denied bail.
Matar's lawyer told CNN that Matar was being cooperative. Matar will appear in court on August 19 at 3 p.m.
The president and the first lady were shocked and sad by the attack.
"With his insight into humanity, with his unparalleled sense for story, with his refusal to be intimidated or silenced, Rushdie stands for essential, universal ideals," Biden said. It's truth. There is courage. It is possible to be resilient. Sharing ideas without fear is something that can be accomplished. These are the things that make up a free and open society. Today, we reiterate our commitment to those deeply American values in solidarity with Rushdie.
Since the publication of "The Satantic Verses" in 1988, the author has faced death threats over his controversial writings.
The fatwa calling for Rushdie's assassination was issued in 1989.
The New York State Police said at a news conference on Friday that there was no reason for the attack.