The student, Maisha Momtaj Meem, was traveling to campus on her scooter when the van hit her while flying over Kuril in the capital on Friday morning.
Iftekhairul Islam, another Dhaka Metropolitan Police Deputy Commissioner, said driver Saiful Islam was arrested in Chattogram around 10 p.m.
Police also arrested Moshiur Rahman, a representative of the company that owned the goods on the van. Moshiur was in the vehicle during the accident.
Iftekhairul said he identified the covered van from security camera footage and traced it through the company operating it.
The vehicle was seized and the two detainees were taken to Dhaka, he said.
Meem, 22, was in her second year of college majoring in English.
She was found lying in a pool of blood next to her scooter during the flyover. The incident was reported to the police during a call to 999.
She was then rushed to Kurmitola General Hospital, where the doctor pronounced her dead. His body was then taken to Suhrawardy Medical College Hospital for an autopsy.
Meem was the eldest daughter of Nur Mohammad Mamun, principal of Mouchak Ideal Public School and Middle School. She lived with her family in Sector 6 of Uttara.
Citing witnesses, his cousin Zakir Hossain said a covered van hit Meem.
His father was admitted to Kurmitola hospital after falling ill on hearing the news of Meem’s death, his uncle Mokhlesur Rahman Badal said.
She was buried in their native village at Mushak of Gazipur.