The driver was tested for alcohol and has not made any statements, sources said.
NY mayor Bill de Blasio said: "Based on the information we have at this moment, there is no indication that this was an act of terrorism".
News outlets said the suspect was a 26-year-old male from the city's Bronx borough.
"It is believed to be an isolated incident, it remains under investigation", the department added on Twitter.
Action News has learned the name of the victim killed in the crash in Times Square Thursday afternoon.
However several witnesses have claimed that the crash was "intentional".
Navy records show Rojas spent two months in a military prison in Charleston, South Carolina, in the summer of 2013 but do not specify why.
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Rojas was in custody and unable to comment.
Police say Elsman's 13-year-old sister was among the people who were struck but survived.
"It was terrible, and you could just see, he didn't stop. It didn't seem like it was going to stop".
The vehicle came to rest on its side on the northwest corner of 45th Street and Broadway - its front end damaged and its trunk cracked open. This happened around lunch time, where tourists and employees typically flood the streets. The 23rd and 42nd Street exits on the FDR Drive are also closed. With the advent of summers, it is peak tourist time in one of the most popular destinations in the world.
Rojas possibly has a history of psychiatric problems and claims to have heard voices in his head before mowing down 23 people in Times Square, NBC reported. I was in shock.
"I'm shaken", said Long, who wasn't injured. "There were people on the ground all the way down the block to our left, and all the way down the block to our right". I was briefed at the scene by Commissioner O'Neill and saw firsthand the professionalism and diligence of New York's first responders.
When Long went outside and looked in the direction the auto had gone, she saw at least six people lying on the ground, including a woman lying face-down with blood coming from her head. "Our prayers are with all of them".
This is a developing story. Check back for updates.