The first incident occurred in Mammanti village, 15 kilometres (10 miles) east of Maiduguri.
Babakura Kolo, who assists the military with security against the jihadist insurgents, said the first incident occurred in Mammanti village, 15 kilometres (10 miles) east of Maiduguri.
"Three female suicide bombers were intercepted by the vigilantes while trying to sneak into the village around 5:00 am (0400 GMT), just as the morning prayers were about to start," he told AFP.
"Two of the bombers blew themselves up while the third was shot dead by a soldier before her explosives detonated. One vigilante was killed and another injured," he said.
Another member of the civilian joint task force, who did not want to be named, said there was a second attack in Mainari, 10 kilometres west of the city at about 8:30 am.
"A male suicide bomber approached the village but some vigilantes got suspicious of his movements and accosted him," he said.
"Suddenly, he blew himself up among the vigilantes, killing three and injuring two."
Maiduguri, the capital of Borno state and the birthplace of Boko Haram, has been repeatedly targeted in the bloody, eight-year insurgency, even as the military regains control of the region.
Suicide attacks on "soft" civilian targets, as well as security checkpoints have increased after the militants were pushed out of captured territory since early 2015.
The conflict has killed more than 20,000 people since 2009 and displaced more than 2.6 million from their homes.