A minor spat turned deadly as the drunken police officer was himself gunned down as a team of other officers arrived at the scene, Federal Police Commissioner Zeynu Jemal told local media.
The attacker was intoxicated with alcohol at the time, Zeynu concluded.
Recent report of ethnically–charged violence in Ethiopia is some of the reasons alluded to the attack but there has been no official statement to reflect this.
Residents said roads in the central district where the shootout occurred were cordoned off but by 0630 GMT, calm appeared to have returned to the area.
Since Ethiopia's Prime Minister Abiy Ahmed took office in April he has undertaken a series of major reforms including making peace with arch-foe Eritrea, freeing political prisoners, pledging to open up the state-controlled economy and promising to overhaul the security services.