The blasts hit a densely populated area of the city and sent residents fleeing in panic.
Witnesses said thick smoke enveloped the sky after the twin explosions, which occurred just two minutes apart.
"The first blast happened at 6:15 p.m. and targeted residents... Other residents mobilised to the scene to assist the victims and that was when the second blast happened," local resident Buba Ibrahim told AFP.
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Emergency services were at the scene, said a security official who did not want to be named.
"It is too early to say what happened or how many people were killed... it is getting dark, but our men and the fire service operatives are on their way to the scene," he said.
One resident, Ismaila Musa, said buildings had been destroyed in the blasts.
"My house is at Gomari...the blasts shook the foundation of our building and many others nearby," he said.
Local car mechanic Dahiru Sadiq said he was at work when he heard the blasts, which sent him and his customers running for their lives.
"I can see smoke and flames across the road though I don't know which building is on fire," he said.
Maiduguri, the capital of Borno state in the volatile northeast, has been the epicentre of Boko Haram Insurgency since 2009.
In January, a popular telecoms market in the city was rocked with explosion, leaving dozens of people dead.
Boko Haram says it is fighting to create a strict Islamic state in the mainly Muslim north of oil-rich Nigeria, Africa's most populous country.
The group has since 2009 carried out attacks across the north and centre of the country, but the violence has in recent months been concentrated in the northeast, the region where Boko Haram was founded more than a decade ago.
Three states in the region -- Adamawa, Borno and Yobe -- have been under a state of emergency since May, when the military launched a major offensive to quash the uprising.
But the security forces have struggled to contain the violence, and since then more than 1,500 people have been killed according to the UN and figures compiled by AFP. The UN says nearly 300,000 people have been displaced in the region.
Nigeria, Africa's most populous country of 170 million, is divided into a mainly Muslim north and predominantly Christian south.
