The aviation ministry announced the change of date on Tuesday without giving a reason for the move.
It said the closure, which was initially scheduled for February, will enable the government repair its runway.
The decision to shut the airport and divert Abuja-bound flights to Kaduna followed threats by airlines to stop flying to Nigeria's capital.
The Kaduna airport, which is primarily used for domestic flights, recorded 12 flights in December 2015 compared to the 812 recorded in the Abuja airport.
The aviation ministry did not give any reason for the change in the date of the closure. It said the matter will be discussed at a meeting with stakeholders on Thursday, January 5.
The meeting is to brief them on efforts being made to ensure that the use of Kaduna’s airport is "seamless and hitch-free," the ministry's spokesman, James Odaudu, said.
Analysts say the six weeks closure of the Abuja airport, the country's second busiest after the Muritala Mohammed Airport in Lagos, will have a negative impact on the already sickened economy.
The closure implicates that Passengers travelling to Abuja will have to first fly to Kaduna and travel in bus shuttles, guarded by security provided by the government, to Abuja on a road full of pot-holes and where kidnappings have been rampant in the last few years.
Construction giant, Julius Berger, is expected to will carry out the repairs on Abuja's damaged runway.