The arrest of the three, who were paraded in handcuffs at a news conference, followed pressure from Islamists who have organised a march from all over the country to the capital to demand the death penalty for atheist bloggers.
“They have hurt the religious feelings of the people by writing against different religions and their prophets and founders including the Prophet Mohammed,” said deputy commissioner of Dhaka police, Molla Nazrul Islam.
The three could face 10 years in jail if convicted under the country's cyber laws which outlaw “defaming” a religion, Islam said.
He denied the arrests were linked to the planned march to Dhaka set for Saturday.
Home Minister Muhiuddin Khan said the three arrested men were among 84 “atheist bloggers” named in a list handed over by an Islamist group to a government panel probing alleged blasphemy against Islam on the Internet.