Swaziland were due to meet the Seychelles in a two-legged first round tie over the next fortnight but have pulled out because of financial constraints, Swaziland FA officials said.
They now face a fine from the Confederation of African Football and the possibility of being banned from the 2015 event.
The qualifying competition for next year's Nations Cup starts less than two weeks before the 2012 Finals, which are being played in Equatorial Guinea and Gabon from January 21 to February 14.
From next year, the African championships, held every two years, reverts from every even year to every odd year to avoid future clashes with World Cup years.
The 2013 Nations Cup has been awarded to South Africa, 2015 to Morocco and 2017 to Libya. The qualifiers for the 2013 tournament will played on a knockout basis over three rounds between January and October.
With the Swaziland-Seychelles tie now called off, the only first round game is that between Lesotho and Sao Tome e Principe. They meet in the first leg in Sao Tome on January 8 and play the return tie in Maseru on January 15.
Seychelles advance to the second round to meet the Democratic Republic of Congo over two legs in March.