The Takfiri militants attacked the city's suburbs on Wednesday night with anti-aircraft guns and several suicide bombers, said Damian Chukwu, police commissioner of Borno State, of which Maiduguri is the capital.
"A total of 13 people were killed in the multiple explosions with 24 persons injured while one person died in the attack (shooting)," he told reporters, according to Reuters.
Several buildings were set on fire but the military repulsed the fighters after an hour, he said.
Aid workers reported explosions and heavy gunfire for at least 45 minutes in the southeastern and southwestern outskirts of the city. Thousands of civilians fled the fighting.
The raid comes six months after President Muhammadu Buhari said Boko Haram had "technically" been defeated by a military campaign that had pushed many militants deep into the remote Sambisa forest, near the border with Cameroon.
More than 20,000 people have been killed in Boko Haram's campaign to establish a caliphate in the Lake Chad basin. A further 2.7 million have been displaced, creating one of the world's largest humanitarian emergencies.