The blasts injured two persons and happened at about 11.30 a.m. (1030 GMT) near the gates of a hospital where suicide bombers killed three people and injured 16 last Saturday, a military source and a witness told Reuters.
“The second blast occurred two minutes after the first one, killed the bomber and injured two other persons nearby,” said Mohammed Haruna, who helped to evacuate people from the scene.
Maiduguri has been the target of several attacks since Muhammadu Buhari, president of Africa’s most populous nation and biggest economy, made it the command centre for the campaign against Boko Haram militants after being inaugurated on May 29.
It was not immediately clear whether the bombers had been targeting the hospital again or whether the bombs had gone off accidentally.
The hospital is one of the few public buildings in an area called Molai, which is on the outskirts of Maiduguri and where security is not always as tight as in the centre of the state capital of Borno.
Osinbajo was visiting a camp about 10 km (6 miles) away that houses some of the 1.5 million people displaced by Boko Haram during the militant group’s six-year fight to establish an Islamic caliphate in the northeast.