The blasts occurred adjacent to the Navy Hospital inside the BNS Issa Khan Base of navy in Chittagong, Additional Commissioner of Chittagong Metropolitan Police Devdas Bhattacharya said.
Two people have been detained in connection with the multiple blasts which occurred right after the Friday prayers and injured six people, police said.
"We recovered two unexploded bombs from the scene and detained two people for interrogation... A bomb disposal unit of ours (police) went inside (the base)," a police officer told PTI on condition of anonymity.
The Navy and the Inter Services Public Relations (ISPR), however, refused to share any details and asked the media to wait for a formal statement.
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No group has claimed responsibility for the attack.
Bangladesh has seen several violent incidents in recent months, including attacks on foreigners, minority religious places, and secular bloggers claimed by the Islamic State (IS), although the government says the attacks have been carried out by local Islamist radical groups.
The attacks have alarmed the international community and raised concerns that religious extremism is growing in the traditionally moderate South Asian nation.