Local police official Manjurul Alam said early Tuesday that the attack took place on Monday evening when the polling and security officials were returning from the polling station at Baghaichhari in Rangamati district, an area once hit by tribal insurgency.
He said military helicopters carried 11 critically-injured people to a military hospital.
Voting was held in Rangamati to elect local government officials, but some candidates boycotted the polls, citing irregularities.
It was not clear who were behind the attacks. Several armed tribal groups are active in the area.