Ibrahim Abdulkadir of the National Emergency Management Agency (NEMA) in the northeastern city said one of the bombers was killed, while the other was arrested.
"The incident happened at Kasuwar Shanu cattle market this morning. There were two suicide bombers. One accidentally blew herself up while the other was arrested by vigilant soldiers," he said.
No one was killed in the explosion, but several people were injured.
Boko Haram's seven-year insurgency began in Maiduguri, though it has since spread beyond Nigeria's borders to Chad, Cameroon and Niger.
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Monday's attack comes two days after President Muhammadu Buhari claimed the military had finally routed Boko Haram from their Sambisa Forest stronghold.
The government in Abuja and the military have frequently claimed victories against the Islamic State group affiliate but access to the epicentre of the conflict in Borno state -- where Maiduguri is located -- is strictly controlled.
That has made independent verification of official statements about victories virtually impossible.
On December 9, at least 45 people were killed and scores wounded when two female suicide bombers detonated their explosives in a crowded market in Madagali in Adamawa state, also in northeastern Nigeria.
Boko Haram's insurgency has left at least 20,000 dead and forced some 2.6 million others to flee their homes.
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