The Union County Prosecutor's Office said police responded to the restaurant on Route 22 near Gelb Avenue after getting reports of a shooting at around 9 p.m. Saturday.
Officers found seven victims at the fast food restaurant, including one person who was soon pronounced dead, the prosecutor's office said in an update Sunday.
Six victims were treated for non-life-threating injuries amid the large emergency response late Saturday night, they said.
"I got an unconscious witness. I've got one shot in the face ... and I have at least two in the leg," a 911 dispatcher says in audio obtained by CBS News New York.
Officials said the preliminary investigation determined the shooting was not random and there was no ongoing threat to the general public.
"This is an active and ongoing investigation," the prosecutor's office said.
After the shooting, a man told CBS News New York his girlfriend works at the Union Township Chick-fil-A and that she said a group of men entered the restaurant and went directly behind the counter, firing multiple shots.
Another worker's relative said there was some sort of altercation and that Chick-fil-A employees were injured in the violence.
The Union Township Police Department has not confirmed their accounts of the incident at this time.
New Jersey Gov. Mikie Sherrill said she was briefed on the shooting and that "New Jersey stands with the Union Township community."
"We now know that last night's shooting in Union Township tragically claimed one life and left six others injured. Our hearts go out to the victim's loved ones, and we are hoping for the full recovery of those who were injured," Sherrill said.
The governor encouraged the community to "remain vigilant and report any information to local law enforcement."
The prosecutor's office urged anyone with information to contact the Union County Police Department as the investigation continues. Anonymous tips can be submitted by calling 908-654-TIPS (8477) or online at uctip.org, they said.