They have been identified as Jahidur Rahman, 33, Shamin Mahfuz alias Sumon, 38, and Md Ismail Hossain, 39.
Police said they were trying to restructure their organisation along the lines of the al Qaeda.
Dhaka Metropolitan Police's ADC (Media) Saidur Rahman told bdnews24.com that the arrests were made during an early hour raid on Thursday.
Earlier, Joint Commissioner Monirul Islam had said, "They were planning to carry out terror attacks in the capital during the Eid holidays. They had also planned an attack on an Eid congregation."
The arrested men, police said, had confessed during preliminary interrogation to planning to promote the ideals of the banned militant organisations such as the al Qaeda through sabotages and terror attacks.
Meanwhile, a Dhaka court on Thursday remanded the three in custody for for three days.
Dhaka Metropolitan Magistrate Amit Kumar Dey issued the order after the accused were were presented before his court in two cases.
The DMP's Detective Branch Additional Deputy Commissioner Md Anisur Rahman said no lawyer stood for the militants.