The attacks all bore the trademark of terror group, Boko Haram.
Initial reports suggested that 47 people died while 50 were injured.
The Borno State Commissioner of Police, Clement Adoda, however, disclosed the latest casualty figures to the News Agency of Nigeria (NAN).
According to him, “Today, Saturday, explosions through Improvised Explosive Devise occurred at three locations in Maiduguri.
“The first one was at first gate of Baga Road Market, at about 11:44hrs. “The second was at about12:30hrs at Monday Market, while the third was at Borno Express Park at about 12:52hrs.
“So far, reports from the three locations indicate that 58 people died, while 139 persons were injured.”
Witnesses said suicide bombers were behind the attacks.
After being pushed out of the city last year, Boko Haram fighters retreated to the nearby Sambisa Forest from where they launched attacks on villages and towns in the north-east, taking over swathes of territory.
Boko Haram has not yet commented on the latest attacks, but it has used suicide bombers before.
According to reports, the first attack occurred at the city’s Baga fish market.
The explosion was caused by a female suicide bomber on a tricycle, killing 10 people, eyewitnesses said.
Later the city’s Monday Market, near a Department of State Security (DSS) office, came under an attack. A trader there told the BBC that two other female bombers seemed to have targeted the market.
One had a bomb strapped to her body that detonated as she was being scanned at the gate leading into the market, he said.
Another woman exploded the bomb she was carrying in a bag a few feet away, he added.
The third blast was at a busy bus station where a witness told the BBC that 12 people could be seen lying on the ground.
But he said he did not know if they were dead or injured or whether the blast had been denoted by a suicide bomber or planted in a vehicle.
It was immediately difficult to know how many people had died as body parts littered the area.
Near the Monday market, casualties were loaded onto waiting ambulances.
“I have counted five ambulances that have evacuated victims from the scene. Soldiers are shooting in the air and warding off people at the market,” Salisu Yaya, a member of a civilian task force, told Reuters from the Monday market area.
“The death toll has risen to 47, with at least 50 others injured. The dead include women and children,” said Abubakar Gamandi, head of the Borno state fisherman’s union who was at the scene at of the first attack, the Baga market, before moving to Maiduguri General Hospital to help coordinate rescue efforts.
A nurse at the hospital and area vigilante leader, Danlami Ajaokuta, confirmed his account.
Last week, Nigeria’s President Goodluck Jonathan said the tide has “definitely turned” against militant Islamists as Nigerian troops and their regional allies recapture territory.
Saturday’s attacks occurred while he was jogging around the streets of Abuja.