Borno state police spokesman Victor Isuku said the incident occurred when three bombers, a man and two women, tried to enter Umarari village just outside Maiduguri.
"They detonated the IEDs (improvised explosive devices) strapped to their bodies while running to different directions," Isuku said.
Among the dead was a local vigilante and a woman and her two children, he said. Another eight people were wounded.
Ibrahim Abdulkadir, spokesman for the National Emergency Management Agency (NEMA), said the vigilante had tried to prevent the bombers from entering the village.
"The vigilante was trying to stop them and that was when he was engulfed by the bomb and the woman was nearby," Abdulkadir explained.
The three bombers also died in the blasts, he said.
The Borno state capital of Maiduguri is the birthplace of Boko Haram, a radical Islamist group that has killed over 20,000 people and forced 2.6 million from their homes since taking up arms against the Nigerian government in 2009.
The violence has triggered a dire humanitarian crisis in northeast Nigeria and the wider Lake Chad region, which has also been hit by the conflict.
Nigerian troops, with the help of regional forces from Cameroon, Chad and Niger, as well as Benin, have since early 2015 managed to claw back most of the territory lost to Boko Haram in 2014.
But despite claims from the Nigerian military that the group is on the verge of defeat, suicide bomb attacks remain a threat to civilians, particularly in Maiduguri.
Boko Haram's elusive leader Abubakar Shekau made his first appearance in months last week, claiming responsibility for a spate of suicide bombings.
