The deceased was identified as Dr Md Abdur Rakib Khan, 59, director of Raisa Clinic and Diagnostic Centre in Khulna and principal of Bagerhat Medical Assistants' Training School.
It was learnt that the death of a mother after giving birth to a baby at the clinic led to the scuffle.
Saiful Islam, younger brother of the deceased, said one Sheuli Begum was admitted to the clinic for having a cesarean delivery on Sunday morning.
The clinic authority referred her to Khulna Medical College Hospital on Monday morning as she was bleeding excessively after giving birth to a baby.
After reaching KMCH, she was referred to Dhaka as her condition deteriorated.
Finally, she died on her way to Dhaka in the night.
Saiful claimed that some relatives of the patients carried out an attack on his brother at the clinic at 8:50pm on Monday, leaving him injured critically.
He was immediately taken to Gazi Medical College and Hospital and later was shifted to Shaheed Sheikh Abu Naser Specialised Hospital.
Rakib succumbed to his injuries while being treated at Intensive Care Unit (ICU) of the hospital around 6:30pm on Tuesday.
Saiful also alleged that when he approached Khulna Sadar Police Station, he was not allowed to lodge a complaint over the incident.
Contacted, OC Aslam Bahar Bulbul said he went to the spot on information.
Also read: First coronavirus death reported in Khulna