Suspected supporters of the Opposition led by the BNP set fire to a polling centre at Feni's Sonagazi Upazila at around 10:15pm on Friday.
Sonagazi police OC Subhash Chandra Pal said petrol was used to torch rooms of Annadacharan Government School under the Nawabpur Union.
He said locals had rushed to the spot and brought the flames under control.
A room of the school had been damaged in the fire, the police officer said.
In a separate development, polling tools at a voting centre in Chittagong's Sitakunda had been set on fire at around 9:30pm.
Sitakunda Police Station's OC Iftekhar Hasan said bamboos, clothes and chairs that were supposed to be used to make polling booths were torched.
He said the damage was not great since members of the law-enforcing agencies had rushed to the spot.
The 18-Party Opposition alliance is boycotting the general elections demanding a non-party government's supervision in polls.
It had enforced several spells of blockades across Bangladesh in a bid to foil the elections.