A resident of the Morrisania section of the Bronx was walking his dog around 4:30 a.m. Tuesday when the animal began to sniff at one of the packages, a New York City Police Department spokesman said.
The man contacted police, who located several different bags containing what appeared to be a woman's head, a torso and a leg - in various bags dumped around the neighborhood.
The bags were sent to the New York City Medical Examiner to begin the process of trying to identify the contents, the spokesman said.
Investigators had yet to positively identify the victim and were questioning a person of interest in the case, a spokeswoman said later on Tuesday.
Several New York media outlets, citing unnamed sources, reported police were questioning a young adult and suspected the victim was his mother.
"That's creepy, I don't like it at all. It feels like some Freddy Krueger stuff," a 49-year-old building superintendent from the neighborhood told The New York Post newspaper, which first reported on the find.
The superintendent, who was not identified by the tabloid newspaper, said police interviewed neighborhood residents who had seen a car randomly dumping bags in the area recently.
(Additional reporting by Daniel Trotta; Editing by Bernard Orr)