The explosions in the Borno state capital targeted the same Monday Market area where at least 15 people died July 1 in blast blamed on the Boko Haram militant group.
The attack came after the militants seized control of another town in Nigeria's restive northeast.
Health worker Dogara Shehu said he counted more than "45 people killed, some of them completely decapitated" in the Maiduguri blasts in an account supported by another witness.
One senior police officer, who requested anonymity, described the explosion, which happened at about 11:00 am (1000 GMT), as a "powerful bomb", which was felt across the city.
Market trader Usman Babaji told AFP the explosives were hidden in a motorised, three-wheeled rickshaw, which are popular throughout the country.
A second explosion followed moments later as people rushed to the scene of the first bombing to help the injured, witnesses said.
Abubakar Bello, who sells chickens near the scene, said the woman was carrying explosives in a wrapper on her back, in the same way that babies are carried.
"I think it was a deliberate plan to inflict much pain on unsuspecting people because the second explosion went off after many people gathered at the scene of the first one."
Boko Haram will likely be blamed for the blasts, given that it has attacked Maiduguri dozens of times during its five-year fight to create a hardline Islamist state in northern Nigeria.
The Islamist group was founded in Maiduguri more than a decade ago and the city was once the epicentre of the conflict until its fighters were pushed out into more rural parts of the northeast.