The incident occurred around 11:30pm on Wednesday
Madhukhali Police Station OC Shafikur Islam said the attackers set fire to cattle sheds, verandas and piles of jute sticks in Arhparha and Dumain unions early in the morning on Saturday, four days before the start Durga Puja.
No one was reported hurt in the attack.
Police strengthened patrol in the areas, he said.
Madhukhali Upazila Executive Officer Lutfunnahar said, "The incidents might have aimed to spread panic before the Durga Puja. We've beefed up security in the areas."
Madhukhali Fire Service official Chaitanya Samaddar told bdnews24.com that the firefighters doused the fires before any major damage or casualties.