The Alpha Jet, with two pilots on board, left its base in Yola, Adamawa state, on what was described as a "routine operational mission" at about 10:45 am (Local time) on Friday and had been expected back by midday the same day.
"Since then all efforts to establish contact with the aircraft have not yielded any positive result," military spokesman Chris Olukolade said in a statement.
Search and rescue teams are trying to track the location of the plane and contact its crew, he added.
A total of 512 were produced in all for 10 air forces around the world, including Nigeria, Cameroon, Ivory Coast and Togo, according to the Dassault Aviation website.
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Olukolade did not specify whether the missing plane was being used against Boko Haram fighters, but residents living in and around the Yola base told AFP last week that there had been an increasing number of sorties.
Residents in Adamawa and neighbouring Borno state have also reported fighter jets overhead, while the military said it was conducting "highly-coordinated" air and land operations against the rebels.
According to the International Institute of Strategic Studies' "The Military Balance 2014", Nigeria's air force has 54 combat capable aircraft but "very limited op (operational) capability" overall.
It classified its 14 Alpha Jets as training aircraft, which were being upgraded.