They had fled across the border to Bangladesh amid heavy fighting between the Myanmar military and rebel insurgents in Rakhine
They are publishing firm Ba-Dwip's owner Shamsuzzoha Manik, who is also the editor of the compilation book, its marketing division head Shamsul Alam, and printing house Shabdakoli Printers' proprietor Taslimuddin Kajal.
They had been arrested earlier in a case filed under ICT Act for publishing the book, Shahbagh police said on Tuesday.
Police produced the three before the court of Dhaka Metropolitan Magistrate Amirul Haider with a plea for a seven-day remand to interrogate them.
The magistrate granted five days for Manik, two days for Kajal and one day for Alam.