People reported deafening gunfire and explosions late on Wednesday around the time families gathered to eat.
Nigerian army spokesperson Brigadier General Sani Usman has sent out a text message urging people not to panic and saying the situation was under control.
Witnesses in Maiduguri said dozens of people began arriving in town after fleeing attacks on their nearby villages.
Boko Haram is linked to the Islamic State group and began its insurgency in Maiduguri before expanding attacks to the neighboring nations of Cameroon, Chad and Niger. But residents of Maiduguri said the latest attack was the first major assault in quite some time.