Nigeria beat Ethiopia 2-0 to finish second in the pool on four points behind leader Burkina Faso who finished with five points.
It is the first time the defending champions have been booted out of the competition in the first round in 21 years.
The last time Algeria were the casualties. Now, Zambia will be preparing to head back home. Nigeria face Ivory Coast while Burkina Faso will play either Tunisia or Togo in the quarterfinals at the weekend.
Coach Herve Renard started the final Group C match without captain Christopher Katongo.
Burkina Faso have lost their key player Alain Traore to injury while Zambia has also lost Davies Nkausu to injury.