The suspect, Corey Duncan, earlier posted to Facebook his plans to bring a handgun to the rink Saturday, the New York Post reported.
The report said Duncan was hiding in his mother's apartment in The Bronx when a tip to police brought officers to the door.
Writing in caps, Duncan posted, "feds at my door i'm going out with a bang!!!!! take my soul."
But the Post said he meekly surrendered to police after nearly an hour of negotiation.
Witnesses said earlier an apparent feud over a jacket at New York's Bryant Park ice skating rink ended in gunfire in which two people were shot and injured.
The gunman not only hit his apparent intended target, but also a 14-year-old boy who skated into the bullet's path Saturday night, the Post reported.
The teen, Adonis Mera, was hit in the back. Doctors told family members early Sunday "he has no feelings from the waist down," the teen's brother, 29-year-old Jorge Arias, told the Post.
Witnesses described a panic-stricken rink.
"The shots went off and people started jumping over the side of the rink," Andres Seixas, 21, told the Post. "They were climbing over each other to get out."
Police were searching for the gunman, described as in his 20s and wearing dreadlocks, who fled with his friends.
Skaters hobbled through the skate house to escape, many of them shedding rental skates and fleeing in their stocking feet.
"No one could run because they all had skates on," said 29-year-old Raghuram Krishnamachari. "Two minutes later, everyone was gone except one guy lying there on the ice."
The gunman's apparent intended victim, Javier Conteras, 20, was struck in his hand and hip and taken to an area hospital.
The shooting arose apparently from a feud over a coat, witnesses and a police source told the Post.
"He started walking real quick toward the ice, and I heard him say to the two guys with him that he was going to go talk to the guy who tried to steal his coat," Danny Betances, 15, said.
Before opening fire, the gunman was heard to tell Conteras as he skated by, "Give me your jacket," a law enforcement source told the Post.
When Conteras passed the gunman again, "he feels a burning sensation and sees he's bleeding from the hand and hip," the source said.