It is the fourth attack in a week in which at least 162 people have been killed, including four suicide bombers, as Boko Haram Islamic extremists appear to obey an Islamic State group order to step up attacks in the holy month of Ramadan.
Nigeria's homegrown extremist group became the IS group's West Africa franchise earlier this year.
In the most deadly attack, the militants targeted several mosques in Kukawa town on Wednesday, gunning down nearly 100 praying worshippers. Kukawa is 180 kilometres northeast of Maiduguri, the biggest city in the northeast.
The latest attacks took place at Malari village, just outside Maiduguri, and began with an explosion from a teenage girl at the market that killed at least 10 people, said security guard Abba Shehu.
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Minutes later a woman in a taxi blew up at a military checkpoint and killed a soldier and two passengers.
Boko Haram took over a large swath of northeastern Nigeria last year and stepped up cross-border raids. Nigeria and its neighbours deployed a multinational army that forced the militants out of towns and had them hemmed into the Sambisa Forest.
But bombings and village attacks have increased in recent weeks.