Re-poll was necessitated at these constituencies following violence and disruption during the January 5 general election.
The Election Commission said voting started at 8 am (local time) and ended at 4 pm.
Election Commission officials said no trouble had been reported from any polling station.
Bdnews24 quoting police reported that six persons were detained in Lakshmipur district for allegedly trying to rig vote.
Many polling stations witnessed almost no voters in the morning due to heavy fog and chilly weather but the number increased as the day progressed, poll panel officials said.
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The Awami League swept the general election following a boycott by the main opposition Bangladesh Nationalist Party (BNP).
The BNP-led 18-party opposition alliance boycotted the polls, demanding a neutral caretaker regime to oversee them.
The opposition tried to derail the polls by calling strikes and blockades. Over 160 people were killed in poll-related violence since November.