The security sources said the blast went off a few meters from the office at about 7 am local time (0600 GMT). One of the security sources said one person was killed, as well as the bomber, while a hospital source said four people were being treated for injuries, Reuters reported.
The city, the birthplace of Takfiri militant group Boko Haram, is frequently hit by bombings.
It has been the target of several attacks since Muhammadu Buhari, president of Africa's most populous nation and biggest economy, made it the command center for the campaign against the militant group after being inaugurated on May 29.
Two suicide bombers blew themselves up near a Maiduguri hospital during a visit by the vice president at the start of July and, a few days later, Boko Haram militants attacked the city from the outskirts.