The teenager was taken into custody at a house police believe may be linked to a family member in Yonkers nearly 24 hours after the shooting that began in a sports shop and spilled out on to the street in Manhattan.

At a press conference announcing the arrest on Friday evening, New York City Police Commissioner Edward Caban said it was an "actual miracle" that no one was seriously injured in the shooting.

"In the middle of the busiest, most highly trafficked part of this city, a criminal with a firearm decided to pull the trigger," he said.

Hours before, police identified the suspect as a resident of a migrant shelter in Manhattan who arrived in New York from Venezuela late last year.

He is also considered a suspect in an armed robbery in the Bronx and a separate shooting in Times Square last month, police said.

Police said the alleged shooter and two other youths were attempting to steal a jacket from the store shortly after 7pm when they were confronted by a security guard who asked to see a receipt.

When the trio couldn't produce one, the guard took back the merchandise.

At that point, the teenager allegedly pulled out a handgun and fired at her, missing the security guard but wounding 38-year-old Brazilian tourist Tatiele Ribeiro Lemos, who was waiting by the cashier to buy a pair of trainers.

In an interview with Sky News' US partner network NBC News, Ms Ribeiro Lemos described the "scary moment" when she realised she had been shot.

"I started checking myself then looked at my leg and saw blood dripping down, but I was able to stay calm," she said in Portuguese. "I believe this was just an unfortunate incident, it could have happened anywhere in the world."

She received 13 stitches for the wound at a nearby hospital.

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The teenager and one of the other youths with him then ran off into the city.

A pair of officers spotted them four blocks away on 47th Street and took the second youth into custody.

The teenager fled toward 6th Avenue with one of the officers giving chase, at one point cutting between buildings. There, he turned and fired at the officer, police said.

"Our officer draws his weapon. He cannot fire," NYPD Chief of Patrol John Chell said at a news conference on Thursday evening. "Too many people around, there's too many people ducking."

The teenager fired again from under his arm and continued to flee, running into a subway station. Surveillance video showed him moving towards the tracks and emerging back on to the street, Chief of Patrol Chell said.

On Friday morning, a third suspect, who is 16, was arrested.

Police said they spoke to hundreds of people and obtained surveillance photos of the alleged shooter leading up to his arrest on Friday.

It is unclear whether the teenage suspect has a lawyer who is able to speak on his behalf.