A statement by ASP Mariam Yusuf in Abuja said the incident happened on Saturday at the Police Divisional Headquarters in Dutsen Alhaji area of the territory.
She said that preliminary investigation into the incident revealed that the inspector fired a shot at the corporal and injured a Deputy Superintendent of Police before committing suicide.
Yusuf said the Commissioner of Police in Charge of FCT, Mr Bala Ciroma, had ordered a discreet investigation into the incident and put measures in place to forestall future reoccurrence.
She said the command commiserates with the family of the deceased and urged residents to remain calm.
Yusuf pledged the commitment of the command to provide adequate security during the Yuletide, NAN reports.