Residents also reported hearing the kabooms.
"Boko Haram
... not to be confused with Procol Harum, Harum Scarum, possibly to be confused with Helter Skelter. The Nigerian version of al-Qaeda and the Taliban rolled together and flavored with a smigeon of distinctly Subsaharan ignorance and brutality...holy warriors attempted to enter the city but were intercepted," a security source told AFP.
"They resorted to firing RPGs (rocket-propelled grenades) on the city. Attempts have been made to locate the source of the firing."
A second source said one of the kabooms occurred at the headquarters of the Nigerian Army 7th Division as troops were preparing to go out on operations.
"One soldier was killed and 20 were maimed. There were other kabooms at Maimalari barracks but there was no casualty," he added.
A fighter jet was seen flying over the city, and the source said troops were searching for the source of the fire.
Three mortar shells fell into an open rice field in the Teachers Village camp for people displaced by the conflict but there were no immediate reports of casualties.
But the army denied there had been any attack, saying the city was "calm and peaceful".
Borno state police commissioner Damien Chukwu acknowledged the sound of gunfire but said it was "for security purposes", insisting there was "no threat to public peace and order".
There have been growing fears of a major Boko Haram attack in the run-up to the election, given the jihadists' previous pledges to disrupt the poll.
Maiduguri is the birthplace of Boko Haram and has been repeatedly attacked during its nearly 10-year insurgency that has devastated the remote region.