Voting has been suspended in the centre, Presiding Officer Alamgir Hossain said.
Around 25 people entered the Hajrakati Government Primary School centre around 11am on Saturday and exploded bombs before snatching a ballot box, he said.
They took the ballot box to a nearby garden and set it on fire, Hossain said.
The criminals also damaged two more ballot boxes of the centre, the presiding officer said.
Police constable Abdul Jabbar was injured when he tried to stop the criminals.
Police fired several shots to control the situation.
Miscreants have set a ballot box on fire in a polling station at Monirampur in Jessore hours after the start of the Upazila elections.
Jessore’s Assistant Returning Officer Sharif Nazrul Islam said told reporters that voting will remain suspended at the polling centre until further orders.
According to injured policeman Jabbar, 10-12 Awami League supporters entered the polling centre around 10:30am, snatched ballot papers and started stamping them.
“They exploded two bombs and fled when police intervened. Moments later, supporters of Jamaat-backed candidate attacked the centre,” he said.
Jessore BGB chief Matiur Rahman said: “Activists of Jamaat-e-Islami exploded bombs and snatched the ballot box before setting it on fire.”
The chairman aspirants in the Upazila are Awami League-backed Amjad Hossain Lablu, Jamaat supported Gazi Enamul Haque and BNP-backed SM Mashiur Rahman.
Jessore Jamaat Secretary Nurun Nabi and Monirampur BNP leader Shahid Iqbal alleged that ruling party supporters stopped others from entering voting centres in several Unions including Chaluyahati, Hariharnagar and Kanchpur.
Jessore’s Additional Superintendent of Police KM Ariful Haque, however, denied the allegations of voting centres being taken over.