The violence occurred in Lalmonirhat when supporters of the Jamaat-e-Islami party were confronted by riot police.
Jamaat-e-Islami had called for a nationwide strike. Three of the people killed were identified as party activists, bdnews24.com said.
Police said the strikers threw Molotov cocktails at passing vehicles and felled trees to block roads in the city. They then turned on riot-squad officers who arrived armed with rubber bullets and tear gas to break up the crowds.