It is the fourth suicide bombing this month in Maiduguri, which is the birthplace of the Boko Haram Islamic extremist group.
Fishmonger Idi Idrisa said one teenager exploded as she approached the mosque crowded with people from the nearby Baga Road fish market, performing afternoon prayers during the holy month of Ramadan.
The second teen appeared to run away and blew up further away, killing only herself, he said.
Civilian defense fighter, Sama Ila Abu, said he counted at least 30 corpses as he helped to collect the dead.
Both men said said there were many injured being sent to the hospitals.
Boko Haram has kidnapped hundreds and hundreds of girls and women and the numbers of female suicide bombers has raised fears that it is using the captives in its campaign.
A military bomb disposal expert has told the AP that most bombs carried by girls and women have remote devices, meaning the carrier cannot control the explosion.
Boko Haram has stepped up attacks since Nigeria's new President Muhammadu Buhari announced the military command center is moving from Abuja, the capital in central Nigeria, to Maiduguri, the capital of Borno State.
The attacks come as Nigeria and its neighbors are preparing to strengthen a multinational army that this year drove Boko Haram out of the towns and villages where it had set up a so-called Islamic caliphate.
But bombings and hit-and-run attacks have continued, along with cross-border raids.
On Thursday, a group of the extremists attacked two towns in neighboring Niger, setting homes ablaze and killing at least 40 people, the government said.
In its first attack on Chad, suicide bombers a week ago simultaneously attacked two buildings including the national police academy in N'Djamena, the Chadian capital, killing at least 33 people and wounding more than 100 others.
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