The clash between Awami League (AL) and its youth affiliate, the Juba League erupted around 1pm on Wednesday at Trishal Upazila's Baliparha Union.
Trishal police OC Maniruzzaman said that a 'turf war' was behind the clash.
The dead has been identified as 40-year-old Saiful Molla, who was an activist of the ruling party's Balhiparha unit, according to police and locals.
OC Maniruzzaman said he died of injuries inflicted by sharp weapons.
Those injured have been taken to the state-run hospital in Trishal and the Mymensingh Medical College Hospital.
Police are yet to provide any other details of the incident.
Balhiparha locals said supporters of UP Chairman and Balhiparha Union AL unit chief Golam Mahmud Badal and local Juba League leader Abdul Bari clashed with sharp weapons.