The authority, called skeyes, said it is forced to shut down Belgian airspace from 10:00 pm (2100 GMT) Tuesday until 10:00 pm Wednesday.
It said in a statement that it "does not have sufficient insight into the staffing levels during the industrial action that will start tonight."
Belgian rail and other public transport systems are due to be hit hard during the 24-hour strike called by unions after the breakdown of wage talks. Police, postal and hospital services will also be affected.
International trains like the Eurostar, Thalys and TGV services are unlikely to be disrupted.
An estimated 650 flights pass through the main Brussels airport each day. Authorities there have warned that no flights will be operating and have asked passengers not to come to the airport.
The airport in the nearby city of Charleroi, which handles about 140 flights daily, had already been ordered closed on Wednesday due to the strike.
European air traffic authority Eurocontrol will manage all flights over Belgian territory above an altitude of 7,500 meters (24,600 feet).