The incident was reported on Friday from the Chittagong-Khagrachari Highway at Hathazari Upazila, said local police OC Belal Uddin Jahangir.
The fire service rushed to the scene soon after the crash around 8am at the Upazila’s Mirer Haat area.
Two bodies were recovered from the scene while two people were taken to the hospital with injuries.
The deceased have been identified as 60-year-old Rokeya Begum and her son 40-year-old Abdul Mannan, said police.
The injured, identified as 27-year-old Sabur and 30-year-old Ashraf Siddique, have been admitted to the Chittagong Medical College Hospital.
“An armoured personnel carrier in the convoy veered off the road and fell into a ditch along with the two autorickshaws,” he told bdnews24.com.
The Inter-Service Public Relations Directorate or ISPR confirmed the crash.
“The convoy was heading to the field firing range in Hathazari. Army personnel are at the crash site. The injured have been taken to the hospital,” ISPR Director Lt Col Rashidul Hasan told bdnews24.com.