They had fled across the border to Bangladesh amid heavy fighting between the Myanmar military and rebel insurgents in Rakhine
The accident occurred near Totar Bazar around 3pm on Friday, Charjabbar Police Station OC Shahed Uddin told bdnews24.com.
The dead are 21 sepoys Mamun Khandaker, Firozul Islam and Fooyez Uddin of the 21st Engineer Battalion in Sylhet.
The vehicle, a pickup, was on its way from Cumilla Cantonment to Sandwip in Hatia when it fell into the canal leaving 11 members of the army injured.
Police and Fire Service rescued the injured and took them to the local Upazila health complex where the doctor declared Mamun, Firozul and Foyez dead, the OC said.
The eight others were airlifted to the Combined Military Hospital in Dhaka by helicopter, he added.