A civilian militia source in the Borno state capital, Maiduguri, told AFP “at least 13” blasts were heard throughout the city at about 6:00am (0500 GMT).
Residents also confirmed hearing the explosions while one of two security sources said: “Boko Haram terrorists attempted to enter the city but were intercepted.
“They resorted to firing RPGs (rocket-propelled grenades) on the city. Attempts have been made to locate the source of the firing.”
The second source added that one of the explosions happened at the headquarters of the Nigerian Army 7th Division as troops prepared to go out on operations.
“One soldier was killed and 20 were injured. There were other explosions at Maimalari barracks but there was no casualty,” he added.
“Troops are out searching for the location of the firing.”
Three of the mortars fell in an open rice field in the Teachers Village camp for people displaced by the conflict. But there were no immediate reports of casualties.
A fighter jet was seen flying over the city in the search for the source of the attacks.
There was no official comment from the military but Borno police commissioner Damian Chukwu denied any attack.
There was “no threat to public peace and order”, he said.
“The gunfire was not targeted at members of the public but was for security purpose,” he added.
Fears of a major Boko Haram attack have been growing in the run-up to elections, which the jihadists have previously vowed to disrupt.
Maiduguri is the birthplace of Boko Haram Islamists and has been repeatedly attacked during their nearly 10-year insurgency that has devastated the remote region.
Voting began from 0700 GMT, with President Muhammadu Buhari, a former army general who has vowed to defeat the jihadists, seeking a second term.
Security sources meanwhile reported clashes between the military and suspected Boko Haram fighters in Auno, on the border of Borno state with neighbouring Yobe.
An attack in the town of Geidam, north of the Yobe state capital Damaturu, also forced residents to flee, they added.
The early morning explosions in Maiduguri come after a Boko Haram attack late on Friday on Zabarmari village, 10 kilometres (six miles) outside the city.
Boko Haram’s insurgency in northeast Nigeria has killed more than 27,000 people and left 1.8 million homeless, creating a humanitarian crisis.
But the government and military have repeatedly said the jihadists are weakened to the point of defeat, despite persistent hit-and-run raids and suicide bomb attacks.
Recent months have seen an increase in attacks against troops, blamed on or claimed by Boko Haram’s Islamic State West Africa Province (ISWAP) faction.
The IS-backed group is known to operate in northern Yobe state and around the border with Borno state.