The deceased was identified as Lance Corporal Shafiqul Islam alias Shafique, 42.
The injured include Sergeant Atiqur Rahman, Corporal Azizul Haque and sepyos Nadim, Imran, Tariqul, Russel, Faisal, Afzal, Raju and Arif.
The injured were first taken to Dumuria Health Complex and then shifted to Khulna Medical College Hospital.
Later, six of the injured were airlifted to the Combined Military Hospital in Dhaka, said an ISPR release.
Mohammad Mahmud, officer-in-charge of Kharnia Highway Police Station, said the truck carrying 27 army personnel skidded off the road and plunged into the ditch around 3:30pm while approaching the Baliakhali Bridge on Khulna-Satkhira road after one of the front tyres got deflated.
The army team was going to Satkhira from Barishal for the winter drill when the accident took place, he said.
Aminul Islam Biplab, officer-in-charge of Dumuria Police Station, said police and firefighters were trying to salvage the truck.