A constable was also injured in the gun battle that took place early on Tuesday.
Injured Muhayeed Hossain, 28, was admitted to the Jessore Medical College and Hospital.
Police raided an area near Hamidpur Moilakhana on a tip-off that activists of Shibir, student wing of Jamaat-e-Islami, gathered there to hold a meeting, said Kotwali Police Station OC Emdadul Haque Sheikh.
Sensing police presence, the Shibir activists opened fire on the law enforcers, injuring constable Bulbul.
As police retaliated, Hossain was shot in his leg.
The others fled the spot.
Police recovered a gun and bullets from the Shibir activist, the OC said.
However, Hossain alleged that police had picked him up from his house and fired at him.