Lawrence Campbell, 27, allegedly slashed security guard Pierre Monsanto in the face at the drug store before going outside and opening fire on police.
Officer Melvin Santiago was shot inside his marked patrol car while responding to the incident at 4 a.m.
Campbell was also killed in the incident after being fired upon by other police officers.
"Watch the news later. I'm going to be famous," Jersey City Mayor Steve Fulop said Campbell told a customer at the drugstore before opening fire on Santiago.
Santiago and his partner were the first on the scene.
A witness to the incident said Campbell had an accomplice, though police haven't confirmed that information.