Soldiers shot dead one woman as she tried to get into the informal market at the base of 333 Artillery Nigerian Army in Maiduguri last evening.
Borno state police spokesman Edet Okon said the woman's explosives detonated when she was shot. A second bomber blew herself up in a nearby motorised rickshaw, he added.
A bomb disposal team had "sanitised" the area, he added.
Emergency services in the city said they had no further information on the blast, which came just days after nine soldiers were killed in a Boko Haram attack north of Maiduguri.
Markets on the fringes of military barracks typically sell basic needs to soldiers, including food and alcohol, and are often frequented by troops as well as civilians.
Police said the blasts happened at 8:20 pm (1920 GMT) but AFP has been told it occurred about 30 minutes before the night-time curfew in Maiduguri at 10:00 pm.
Suicide bombers, many of them women and young girls, have previously targeted security checkpoints, as well as markets, mosques and camps for those displaced by the insurgency.
The government, which maintains Boko Haram is on the verge of defeat, wants IDPs to return home.
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