The airports will be reopened on 21 June.
The five are located in the capital Abuja, the commercial hub Lagos, the southern city of Port Harcourt, the northern Kano state and south-eastern Imo state.
Musa Nuhu, the head of the aviation authority, said other airports "will be gradually added to the network after a review and assessment".
"The closure of Nigerian airports to international flights will continue until date of the resumption is announced," he said in a statement.
Flights repatriating Nigerians from abroad and humanitarian flights are allowed to operate, but under strict protocols.