General Constable Owusu Frimpong died in the early hours of Thursday at the Nalerigu Baptist Medical Center where he was admitted after he and two others were shot last Sunday.
There were on patrol duty when they were ambushed by criminals suspected to have been organized by Johnson Kombian Gakum.
General Constable Prince Agyare died in the attack and Lance Corporal Osei Bonsu was injured.
Chief Inspector Ebenezer Tetteh, the Northern Regional Police Public Relations Officer, told the GNA that General Constable Frimpong's body would be sent to the Police Hospital in Accra for autopsy.
The police administration had announced a GHc3, 000 reward for anyone who would volunteer information leading to the arrest of Johnson Kombian Gakum.