Fire fighters were called to All Saints Church at around 5:30 yesterday evening.
Crews had to battle the flames at the church for more than three hours before the fire could be brought under control.
An aerial ladder platform was also used to help dampen the blaze.
Police said the 17-year-old had been released on bail.
A spokesperson for the Diocese of Guildford said: "The news of the fire at All Saints Church in Fleet is alarming, and our immediate prayer is that everybody within the vicinity is safe and sound, and for members of Hampshire Fire and Rescue Service who are tackling the blaze.
"The sudden loss of a church building can have a far-reaching effect on a community, beyond those who attend regularly, and so our thoughts and prayers are also with the Vicar and everyone in the congregation and town of Fleet."
Officer in charge of the incident, Group Manager Brian Rudman said: "This was a significant fire that has seriously affected a beautiful and historic building. Crews have worked hard in arduous conditions to bring the fire under control.
"Unfortunately the roof of the church has been completely destroyed by the fire but the main structure and brick work remains intact and there is every hope that this church can be rebuilt in the future."