The attack on the northeastern city began just after midnight on Saturday and left at least eight people dead, with 27 injured.
A raid on the town of Monguno, north of Maiduguri, was reported later in the morning.
Nigeria’s defence headquarters said that they were coordinating land and air operations to repel the attacks and a curfew was in place.
Security sources told Reuters that Boko Haram attacked the outskirts of the city and tried to take the airport. The Islamist group last attempted to take Maiduguri from the same area in December 2013.
Boko Haram are blamed for killing thousands of people, mostly in north-eastern Nigeria. The 200 Chibok schoolgirls kidnapped by the group last year made headlines around the world, and are still missing.
Earlier this month Boko Haram attacked the towns of Baga and Doron Baga. Satellite pictures released by Amnesty International showed the extent of destruction.
The government said 150 people had been killed in the attacks but local officials say the figure is far higher and some have put it as high as 2,000.
The group has seized swathes of new territory in the run up to Nigeria’s presidential elections – due to take place of 14 February.
The elections are expected to be the most hotly contested since the end of military rule in 1999 with many fearing violence in the aftermath.
US Secretary of State John Kerry arrived the country on Sunday to urge the candidates and their supporters to respect the election outcome, underscoring US concerns that post-poll violence could destabilise the country and undermine the fight against Boko Haram.
“Given the stakes it’s absolutely critical that these elections are conducted peacefully,” said Kerry. He also urged Nigeria to hold its elections on time, after some reports suggested the government might try to delay the poll.