The deceased was identified as Imtiaz Hasan Mahin, 14, son of Md Ilias and class-VIII student of Agrabad Kolokakoli High School.
Soyedul Alam, a sub-inspector at Double Mooring Police Station, said Mahin along with his friends were sitting near a department store in the evening.
At one stage, he locked into an altercation with a staff of the shop, Shahed, 15, around 8pm over a trifling matter, the SI said.
Later, Shahed stabbed Mahin indiscriminately, leaving him critically injured.
Mahin was taken to Chittagong Medical College Hospital where he succumbed to his injuries.