It comes after airlines threatened to stop flying there because of safety concerns over the state of the runway.
From now, those wishing to travel to Abuja are being encouraged to instead fly to the northern city of Kaduna, 190km (120 miles) away.
But all but one international airline has refused to fly there.
Ethiopian Airlines is currently the only company offering international flights to Kaduna, which has been hit recently by a spate of kidnappings.
The government has set up a dedicated Abuja Airport Closure website, where passengers can book free bus tickets for the two-hour journey by road.
"The runway has deteriorated to such an extent that it requires complete reconstruction," the government said.
"This cannot be done at night. Furthermore, the runway has been maintained mostly through closure at night in the past several years, but is has reached a state where that method will not work anymore."
What are people going to do?
All domestic flights are being rerouted to Kaduna, a small regional airport.
The shuttle bus to Abuja will take two hours on a good day, more with traffic. Like most Nigerian roads it is bumpy but the government has undertaken some repairs on it in preparation for the airport commuters.
On the international front however there are not many options.
Most international airlines said they were worried about security. Some also expressed concern that the equipment at Kaduna airport was not of a high enough standard.
Henrietta Yakubu from the Federal Aviation Authority of Nigeria told the BBC's Focus on Africa programme that plans had been put in place to protect passengers and to transfer them in luxury buses.
"The police boss has assured members of the public that for each luxury bus on the highway, there will a police patrol vehicle on the front and behind," she said.
"A police checkpoint will also be set up every one kilometre on the road between Kaduna and Abuja."
Is it safe to fly to Kaduna?
In February two German archaeologists were kidnapped while working on a dig near the Kaduna-Abuja road. That sounded the final death knell on efforts by the Nigerian government to convince international airlines to fly there.
The government has promised extra security on the Abuja-to-Kaduna highway but that will not reassure many passengers or airline bosses.
Even in Lagos and Abuja they hire police escorts for their crew. Southern Kaduna has also been in the news recently over ethnic clashes between farmers and Fulani herdsmen which may put some passengers off travelling there.
However that conflict is further west in very rural areas and unlikely to spread to the Abuja-Kaduna road.
Could I go to Lagos instead?
The airport in the commercial capital, Lagos, has more international flights than Abuja but it would be a 12-hour drive to Abuja, at the very least. Though it may be safer, the Abuja-to-Lagos road is in terrible disrepair.
Some embassies in Abuja have talked about the possibility of flying to Enugu, a six-hour road trip from Abuja, in case of an emergency.
What will the impact be?
It is hard to tell just what impact the closure will have or how many people will choose not to fly. Nigeria's biggest airline Arik has introduced a reduced schedule.
But flying in Nigeria is incredibly unpredictable anyway, with flights often delayed for hours and then cancelled.
Nigerian air travellers are already extremely resilient and will most likely weather this latest storm just fine.
However, it is also likely to affect Nigeria's postal service, as 40% of the country's international mail is transported through Abuja.
How bad is the Abuja runway?
It is bad. There are two major holes in the runway and several serious cracks and bumps.
In August a South African Airways plane damaged its landing gear when it hit one of the potholes. Although no-one was injured, the plane was out of commission for four days.
Many of the major airlines threatened to stop flying if the runway wasn't fixed.
Why did it get so bad before anything was done?
Successive governments have ignored the problem for more than 15 years. The runway was supposed to be upgraded in 2002 - it was built in 1982 and was only meant to have a 20-year lifespan.
That is because of a cocktail of corruption and incompetence on the part of those in charge. But with gaping potholes now posing a real danger, the problem is impossible to ignore.
