The operative was said to be attached to the Borno Geographic Information Service (BOGIS) that was on a demolition exercise at the church.
A crowd of young people at the premises had staged a protest after the driver of an excavator started destroying the church, including the properties inside.
The task force operative reportedly opened fire on the youths to disperse them, but a bullet hit a man who was identified as Ezekiel Burris.
Sources said the operative, identified as Baba Bukar, has now been taken into police custody, following a directive by Babagana Zulum, governor of the state, to investigate the incident.
Zulum had asked the police to arrest and prosecute anyone connected to the violence which led to the death of Burris.