"For now domestic flights are not taking place as only skeleton services are going on," Yakubu Dati of the Federal Airports Authority of Nigeria (FAAN) told AFP.
Dati said international travel had not been affected, with the major carriers that operate in Nigeria -- including British Airways, Air France and KLM -- continuing with regular services.
The air traffic controllers' union has made a series of demands for better pay and improved working conditions but it was not immediately clear if they issued a warning about their planned work stoppage.
Domestic air travel is a crucial means of transport across Nigeria, Africa's most populous country, given the poor conditions of many roads and relatively limited train network.
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Attacks by roadside bandits who target motorists have also led to an increase reliance on domestic flights.
Nigeria's top domestic carrier, Arik Air, confirmed that it had been grounded.
"We are not flying now because of the industrial action," a company spokesman said, adding that the airline would resume operations "as soon as the issue is resolved."