The law enforcement official had been briefed on the shooting and spoke to The Associated Press on the condition of anonymity because the shooting took place in a different jurisdiction.
The shooting happened around 4 am inside a Pathmark grocery store in Old Bridge, about 25 miles from Manhattan, Mayor Owen Henry told nj.com. The store was closed and had been scheduled to open at 6 am.
Two front windows were broken out early on Friday, and two police cars were pulled up near the entrance. It wasn't immediately clear what broke the windows, nor was it clear whether any store workers were still inside the store.
Employees in the store at the time of the shooting congregated later in the morning outside a TGI Friday's restaurant in the same shopping plaza.
Police at the scene were keeping onlookers well away from the store. A number of vehicles were in the parking lot outside the supermarket, along with police vehicles.
The store and its parking lot were closed on Friday. Pathmark officials had no immediate comment on the shooting.
Old Bridge is a bedroom suburb of about 65,000 just across the Raritan Bay from New York City's Staten Island borough.
New Jersey Transit closed its nearby park-and-ride lot and told riders that they could park in other park-and-ride lots or could ride a different rail line.