The explosion happened near the corner of 5th Avenue and 68th Street, Xinhua quoted city's fire department as saying.
Eyewitnesses said that a man was climbing a rock structure and stepped on something that "exploded," according to local media.
Police and paramedics rushed to the scene after a call came in at 10:53 a.m. local time.
The victim suffered an injured leg and was being treated by emergency responders with "a possible amputation," said a Fire Department of New York spokesperson.
The area affected was a short distance from the Central Park Zoo, a popular tourist spot.
It was not immediately known what caused the blast, but officials said it was believed to be the result of some sort of fireworks, local media reported.