Two more suicide bombers detonated their devices at the gates to a nearby refugee camp, wounding many people, an emergency services official said.
The regional Emergency Agency said 45 people were "critically injured". The death toll could be as high as 30.
In all, at least 83 people were wounded in the three explosions near the city of Maiduguri, the epicentre of the long-running conflict between government forces and Boko Haram.
Nigeria's military last year wrested back large swaths of territory from the armed group. But they have struck back with renewed zeal since June, killing at least 143 people before Tuesday's bombings and weakening the army's control.
The group has waged an eight-year war to create an Islamic state in northeast Nigeria and provoked international outrage by kidnapping more than 200 schoolgirls known as the Chibok Girls in April 2014.
More than 80 of the nearly 200 schoolgirls who were still missing after a mass Boko Haram abduction in northeast Nigeria in 2014 were freed in May in exchange for prisoners.
Its better-known faction, led by Abubakar Shekau, has mainly based itself in the sprawling Sambisa forest and has been characterised by its use of women and children as suicide bombers targeting mosques and markets.
Fiyaso Soyomb, Editor of the International Centre for Investigative Reporting in Nigeria, told Al Jazeera that Boko Haram likes to use female suicide bombers because they are harder to detect.
"Following the trend of attacks, it's clear that there has been an upsurge since the release of [more than 80] girls in exchange for Boko Haram commanders - that's a big factor."
A rival faction - based in the Lake Chad region, led by Abu Musab al-Barnawi and boasting ties to the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) - has in the meantime quietly become a deadly force capable of carrying out highly-organised attacks.
Last month, an oil prospecting team was captured by al-Barnawi's group. At least 37 people, including members of the team, died when rescuers from the military and vigilantes attempted to free them.
The Boko Haram rebellion has killed 20,000 people and forced some 2.7 million to flee their homes in the last eight years.
Source: Al Jazeera and news agencies