Forces of the eastern Libyan National Army (LNA) loyal to Khalifa Haftar struck Misrata's air college early on Tuesday, a military source and resident said.
Misrata is a coastal city that lies to the west of the capital Tripoli and is regarded the main base of the Western Libya forces loyal to the UN-recognized Government of National Accord.
Early reports said the target of the attack was a Turkish drone base.
Turkish President Recep Tayyip Erdogan previously announced that his country supplies the Government of National Accord with weapons under a military cooperation agreement. In response, Haftar vowed to retaliate by targeting Turkish forces.
A Misrata resident said "massive explosions were heard across the city."
A drone air strike on Monday by Haftar's forces on the southern Libyan town of Murzuq has killed at least 43 people, a local official said.