The HC bench of Justice Obaidul Hassan and Justice AKM Jahirul Huq passed the order.
The bench also instructed the law enforcement agencies not to arrest them until the hearing on the anticipatory bail petition is held.
Barrister Amir Ul Islam stood for the petitioner.
The four other accused are Mohitul Alam, senior sub-editor of Kishore Alo, Kabir Bakul, head of Event and Activation, executives Shah PoranTushar and Shubhashish Pramanik.
A Dhaka court on Thursday issued a warrant for the arrest of Prothom Alo Editor Matiur Rahman, Associate Editor Anisul Hoque and eight other people in a case filed over the death of Nayeemul Abrar Rahat.
Nayeemul Abrar, a ninth grader, died after being electrocuted behind the stage at an event organised by Kishor Alo, a publication of Prothom Alo, on the compound of Dhaka Residential Model College on November 1.