According to AP, fierce fighting is said to be taking place on the outskirts of the city, which is mostly populated with Muslims, but is known to have a considerable Christian community.
"It is flying bullets everywhere. All we hear are sounds of guns and explosions," said Buba Kyari, a resident of Moronti neighbourhood, near Jintilo.
"A rocket-propelled grenade hit and killed a person from my neighbourhood who was fleeing into the city."
Maiduguri has become home to tens of thousands of people who have fled Boko Haram attacks in other parts of the region and was visited on Saturday by President Goodluck Jonathan.
According to the government, "Troops are repelling a simultaneous attack on Monguno and Maiduguri by terrorists," the defence headquarters said on Twitter.
Fears have been growing for months about a possible strike on Maiduguri after the Islamist militants began seizing towns and villages in three northeast states about six months ago.
On January 3, they captured the fishing hub of Baga, in the far north of Borno State, which security analysts said put them in a better position to strike south to hit Maiduguri, the state capital.
UK-based human rights group Amnesty International released satellite images of towns attacked by Boko Haram which showed thousands of structures damaged or destroyed in Baga and neighbouring Doron Baga.
Nigeria's government has disputed reports that as many as 2,000 were killed, putting the toll at just 150.
