Rojas enlisted in the Navy in 2011.
Alyssa Elsman died Thursday when a man drove his auto down the sidewalk for three blocks into the heart of New York City's theater district.
"There ones who were critical, they were taking them fast, going on their way, and getting out of here as fast as possible", another witness said.
Rojas, a US citizen and Navy veteran, has a criminal record including previous DWIs. He was being tested for alcohol and drugs, Police Commissioner James O'Neill said.
Rojas has had multiple arrests, including two for driving while intoxicated, according to police.
He was discharged in 2014 as the result of a special court martial, a Navy official said.
In previous arrests, he told authorities he thought he was being harassed and followed, according to a law enforcement official who wasn't authorized to speak publicly on an ongoing probe and spoke to the Associated Press on condition of anonymity.
Police say the Bronx man was being tested for alcohol and drugs.
The driver of a maroon Honda vehicle has been identified as as 26-year-old Richard Rojas, U.S. Navy sailor.
Officials said Rojas's criminal record included an arrest earlier this month in the Bronx for allegedly threatening a notary with a knife who had come to get his signature on financial documents.
"I was just doing something that I hope people would do, because I was trying to do the right thing", he said. Rojas's auto had been repossessed, said neighbor Jose Mederano, adding that he got it back Wednesday night.
He expressed sympathy for those injured and especially for the woman who was killed and her family.
Consulate General of China in NY said in a statement that its officials had asked hospital authorities to provide injured pedestrians' information, adding that so far no Chinese nationals had been reportedly injured in the auto incident.
Annette Proehl, who is from Pennsylvania, was in Times Square with a group of children on a field trip when she heard the speeding vehicle approach, with people screaming.
White House press secretary Sean Spicer tweeted that Trump was briefed before NY authorities confirmed the death.
Trump is holding a news conference at the White House later Thursday with Colombian President Juan Manuel Santos.
Richard Rojas, 26, is accused of steering his auto onto the pavement in the heart of Times Square, driving for three blocks and hitting 23 pedestrians along the way.
Pandemonium erupted when the vehicle barreled through the prime tourist location and came to rest with two of its wheels in the air. Images from Times Square showed several casualties strewn across the pavement. In its aftermath, city street corners were turned into triage treatment areas, CBS New York reports.