Tuesday’s skirmish in the town left at least 10 people injured, said Kurigram Sadar Police Station OC Murshedul Karim Mohammad Ehtesham.
A group of stick-wielding Jamaat and Shibir activists took out a march in support of the BNP-led alliance’s general strike in the morning.
“They hurled stones at us when we tried to stop them, which ensued a pitched battle,” OC Ehtesham said.
“We fired several rounds of rubber bullets and teargas canisters to take control of the situation,” he added.
Jamaat leader Abdul Haq, 54, who is also a superintendent of a local madrasa, was hit by a rubber bullet during the skirmish.
Police arrested Shibir activists Ershadul Haq, 30, and Shahidul Islam, 28, and Jamaat’s Abdul Jalil, 40, at the spot.
The BNP-led coalition has been enforcing an indefinite blockade throughout Bangladesh since January.
More than 100 people have been killed, mostly in arson, during the anti-government agitation for a snap election.