In one of the attacks, a female suicide bomber killed worshippers who went to pray at a mosque.
It was also reported that there were other attacks within the environment. On July 14, 19 people were killed in four near-simultaneous attacks carried out by women.
The woman detonated her bomb while trying to enter the mosque in the centre of Maiduguri, the capital of Borno state, at around 04:30 a.m.(0330 GMT), shortly before early morning prayers, Borno police commissioner Damian Chukwu said.
"The wounded boy was referred to the Specialist Hospital, Maiduguri for medical attention", he said.
A source at the State Emergency Management Agency (SEMA), who confirmed the incident, said only the two boys were affected in the blast.
"Scene was visited and the area rendered safe by police EOD team". Seventeen people were killed in the city last week.
"Unknown to them, the girl was being pursued from another part of town by residents who were suspicious of her movement at the time".
Meanwhile, two female suicide bombers were killed at Mammanti area, an outskirt of Maiduguri.
The attack comes barely a day after a ten-year-old Fulani boy herding cattle was killed while his 8 years old younger brother sustained injuries in an explosion from a suicide bomb belt forcefully strapped around the elder's body by suspected Boko Haram insurgents.
"They came in contact with Boko Haram terrorists elements".
Maiduguri has been repeatedly attacked in recent months, with mosques, markets, camps for those displaced by the conflict and other civilian "soft" targets hit regularly.