Metropolitan Magistrate Amirul Islam Chowdhury made the order after police produced publisher Shamsuzzoha Manik, his office executive Shamsul Alam and printing press owner Taslim Uddin. Police will be questioning Manik for five days, Alam for one day and Uddin for two days.
The arrests followed the shutdown Monday of a stall of the Badwip Prokshan, the publishing house owned by Manik, at a major month-long book fair in Dhaka.
Six books were seized from the stall, police official Abdul Baten told a news conference.
The arrests were made after some readers complained that the books discussed sex and perversion of Muslims.
The recent murders of secular bloggers and a publisher who dealt with Islam and criticised Prophet Muhammad in writings and books have drawn attention to freedom of expression in Bangladesh, a Muslim-majority nation of 160 million people that is ruled largely by a secular system based on British common law.