The first explosion came from a suicide bomber in a tricycle taxi who blew himself up outside a fish market and killed at least 10 people.
"I saw many dead bodies lying on the ground, many dead, and several others badly injured," said fish seller Idi Idrisa.
People are still counting the dead but a security officer said the explosion at Baga fish market was massive. He said he counted at least 10 corpses. He spoke on condition of anonymity because he is not authorized to speak to reporters.
About an hour later a second explosion rocked the area.
The second blast happened at the Post Office shopping area, close to where the first bomb went off, according to witness Baban Musa, who said there were many casualties.
No one immediately claimed responsibility for the explosions but they have all the hallmarks of the Boko Haram Islamic extremist group. It has increased suicide bombings and village attacks recently as forces from Nigeria and Chad have driven the insurgents from a score of towns along Nigeria's border with Cameroon.
Maiduguri is the birthplace of Boko Haram and the extremists have tried to seize the city and have made it the target for many bombings.
Boko Haram also has attacked villages in Cameroon and Niger as Nigeria's neighbors are forming a multinational force to confront the spreading Islamic uprising.
Chad's President Idris Deby this week said his forces know the whereabouts of Boko Haram leader Abubakar Shekau and warned him to surrender or face certain death.
Boko Haram fighters are massing at their headquarters in the northeastern town of Gwoza, in apparent preparation for a showdown with multinational forces, according to witnesses who escaped from the town.
An intelligence officer said they were aware of the movement but that the military is acting with care as many civilians still are trapped in the town and Boko Haram is laying land mines around it.
About 12,000 people have died in the nearly 6-year-old insurgency centered in northeastern Nigeria.