The airport will be closed for six weeks, starting in February 2017.
The announcement comes after airlines threatened to stop flying to Abuja because of safety concerns over the state of the runway.
During the repairs, domestic and international flights to Abuja will be diverted to the city of Kaduna more than 160km (100 miles) away.
BBC Nigeria correspondent Martin Patience says passengers diverted to Kaduna will face a two-hour journey along a road that has recently been hit by a spate of kidnappings.
The hour-long flight from Nigeria's commercial centre Lagos to the capital is used as a shuttle by many businesses.
Critics are warning that the closure will prove hugely damaging to the country's economy, which is already reeling from its worst recession in decades.
But the government says that by carrying out the major work in one go, it will not have to make smaller repairs in the future.