The empty St Michael on the Mount Church on St. Michael's Hill caught fire at about 12:30 BST, Avon and Somerset Police said.
Crews from Avon Fire and Rescue were in attendance and a wide cordon was placed around the area over fears of asbestos in the roof of the property. About 35 firefighters and 15 fire engines were involved as part of the roof collapsed. People living nearby were asked to keep windows and doors closed.
The fire service has since said the fire was started deliberately with about two thirds of the roof being destroyed but the rest of the building was left largely intact. The Grade II-listed building - parts of which date back to the 15th Century - has been empty since the 1990s.
The Diocese of Bristol, which owns the building, said: "St Michael on the Mount Church on St Michael's Hill is a closed church that the Diocese of Bristol working with the Church Commissioners have been managing and seeking a use for.
"We are assisting the Fire Service and the Police with their investigation."
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