The incident happened during a disagreement in the early hours of Thursday.
The incident is reported to have resulted into panic in the area as residents fear a confrontation between both security forces will happen.
According to a report by Vanguard, Rivers Police Commissioner, Zaki Ahmed, confirmed the incident happened in the early hours of Thursday.
"It is very unfortunate, but it is not true that soldiers are chasing police," he said.
A resident who lives in the area where the incident happened said the disagreement had ensued when officers approached the soldier who was armed but not in his uniform.
The resident told TheCable, "Some soldiers lodged in a hotel around Ada George Road. Two of them came outside to get food, and one was with a gun. When the police came, they asked the soldiers to follow them to their station but the soldiers refused and an argument broke out.
"One of the policemen opened fire on the soldier who died in the process and the other one ran back to inform his colleagues."
Police officers have reportedly deserted the Rumuekani Police Station, Ada George Road, Obia Akpor locality of Port Harcourt metropolis in anticipation of a reprisal from Army officers.