The raid, on an apartment in a two-storey building at Hathajari, lasted nearly six hours, said police's Additional Deputy Commissioner Babul Akter.
The arrests come just days after a 15-hour crackdown on a JMB hideout in Dhaka's Mirpur area where six were held with explosive vests and improvised grenades.
An MK 11 sniper rifle, ammunition, explosive gel, detonators, pieces of army uniform, and bomb-making materials were found in the apartment, Akter was quoted as saying by the bdnews24 online.
"The US-made sniper rifle is a highly sophisticated weapon. This is the first time anything like this has been seized in Chittagong," said Detective Branch Sub Inspector Santosh Chakma, a member of the raiding team.
Bangladesh has seen several violent incidents in recent months, including attacks on foreigners and secular bloggers claimed by the IS, although the government says the attacks have been carried out by local Islamist radical groups.
A minority Ahmadi community mosque was attacked on Christmas in Bagmara town, some 250 kilometres from Dhaka, in which 10 people were wounded.
IS has claimed responsibility for the attack.
