Police said the assailants had stopped and hacked Mir Sanwar Hossain near Shishir Math under the Bat Taila union around 10am on Friday while he was on his way to his dispensary on a motorcycle.
Kushtia Model Police OC Shahbuddin Chowdhury said another man named Saifuzzaman was injured in the attack.
Sanwar, who lived in Kushtia town, ran a free Friday clinic at Bat Taila.
Police said Saifuzzaman had been admitted to the Kushtia General Hospital.
Several people said Saifuzzaman was a teacher at the Islami University in Kushtia but police could not confirm the information.
OC Shahbuddin said police was not yet certain who the murders were and about their motives.
The body of the doctor has been sent to the Kushtia General Hospital morgue for post-mortem.