Suicide bombers are believed to be behind the attack.
Explosions were reported from three different locations in the city, which is the capital of Borno state, including a marketplace and the entrance to Maiduguri University Hospital, according to Sirajo Abdullahi, head of the country's emergency management agency NEMA.
It is unclear how many people were killed and injured.
"We cannot give the actual figure," Sirajo Abdullahi said as rescue efforts were underway.
The attack follows suspected jihadists' attack on a military post on the outskirts of Maiduguri on Monday night.
The jihadist movement Boko Haram and the rival group ISWAP have recently escalated their attacks in the northeastern part of the country.
