The incident occurred Wednesday night in Punjab province's Gujrat city, Dawn online reported.
The 45-year-old victim was arrested Tuesday for attacking two people in a locality in Gujrat.
During interrogation, Assistant Superintendent (ASI) Faraz Naveed got into a heated argument with the victim and struck him on the neck with an axe which resulted in immediate death.
Naveed later accused him of making derogatory remarks against Prophet Muhammad, with other police officials saying the arrested man was mentally unsound.
Police have arrested Naveed and have launched a probe into the incident.