The ship carrying the Bangladeshis will bring back Myanmar security personnel who crossed the border recently amid fighting with rebels
Police identified the woman as Rashida Begum but could not give further details.
The mishap took place on the Satkhira-Jessore Highway at Chhaygharia, about 10 kilometres from Satkhira town, on Friday evening.
Rashida and her daughter were crossing the street after getting off an autorickshaw, Sadar Police Station’s Assistant Sub-Inspector Sohrab Hossain said.
They died on the spot.
Accidents are frequent on the busy Satkhira-Jessore highway.
Such mishaps are mainly blamed on unskilled drivers and rundown roads.