The shooting happened on Beverly Street in Newark around 4:00 a.m.
Eyewitness News is told the incident began with a foot pursuit, as police chased the suspect out of Irvington into Newark.
Police say the suspect was caught breaking into a machine shop and escaped.
Officers then caught up with him and a struggle for the officer's weapon apparently ensued.
The suspect wound up shot in the shoulder. He was taken to a nearby hospital, where he later died from his injuries.
The officer has been taken to a hospital, as well, for unknown injuries. Those injuries are said to be non-life threatening.
A police investigation is underway.