The Howell Township Police Department said on Facebook the incident was reported around 3 p.m. on Crooked Stick Court in the Adelphia Greens residential development off Route 9, located about 50 miles south of New York City.
The 6-year-old girl said she was outside playing with friends when most of the other children went inside.
The girl then stayed outside cleaning up toys when a man approached her and placed the bag over her head, according to police.
Police said the girl screamed, spooking the would-be kidnapper, and while he ran away she ran inside her home. She was not injured during the incident.
"It was reported he never tried to grab her," police said.
Howell Township police said the girl described the man to officers as the driver of a black SUV. The man is described as 40 years old with black hair, a beard and a thin build.
He was described as wearing black shorts and a black t-shirt. He took with him the paper bag that he allegedly placed over the girl's head.
A black SUV was observed sitting in a parking space at the development for an extended period of time but was gone by the time authorities arrived.
"We are asking residents to review their security cameras for any footage that may be beneficial," Howell Township police said.
Anyone with information is asked to contact police at 732-938-4111.