The officer was shot in the head during clashes between Palestinian security forces and gunmen in the camp, according to Maan News Agency.
PA forces raided the camp to arrest alleged criminal Ahmed al-Zabour, who is top of Ramallah's most wanted list.
The governor of Nablus, Akram Rajoub, said two other officers were injured in the raid, along with al-Zabour, who is said to be in a serious condition in hospital.
Balata is the largest refugee camp in the West Bank and has often seen violent clashes between Palestinian security forces and residents.
The Palestinian Authority says the arrest raids are part of a security crackdown to restore stability to the area.
Local residents and analysts, meanwhile, say the raids are an attempt to quash anti-President Mahmoud Abbas elements in the camp, part of an internal struggle within the Fatah movement.
Last August, two Palestinian policemen were killed during a raid in Nablus as part of a security crackdown in the West Bank.
PA forces killed three Palestinians in a subsequent man-hunt for the perpetrators, with one suspect beaten to death in police custody.
The UN Human Rights Office in the Occupied Palestinian Territory called the incident an "extrajudicial execution".