Boko Haram, which says it wants to create a strict Islamic state in northern Nigeria, has killed thousands of people in its four-and-half-year uprising and the military has struggled to contain the violence.
According to multiple witness accounts, the gunmen entered Maiduguri after crossing a river on the fringes of the city.
They passed through the residential neighbourhood of Fauri, opened fire on civilians and torched several homes. Details on casualties were not immediately available.
Area resident Dauda Mahmud said the Boko Haram gunmen "came in large numbers".
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Another witness, who requested anonymity, told AFP that "explosions and gunfire could be heard throughout the city."
"We have never heard such explosions in this city for a very long time," he added.
Students at the University of Maiduguri reported hearing sustained gunfire throughout the morning.
"There have been several deafening explosions and unending gunfire for the past one hour," said student Mercy Bitrus.
"The fighting is no doubt taking place near Giwa barracks which is very close to us because the sounds are coming from the direction of the barracks," she added.
The name Boko Haram means "Western education is forbidden" and schools and universities have been repeatedly targeted during the conflict.
Human Rights Watch today said Boko Haram has carried out more than 40 attacks already in 2014 which have killed roughly 700 people.