Harambee Stars chances of making it to the Last 16 of the competition were left in tatters after they lost 3-0 to Senegal in their final Group C match on Monday.
That defeat meant Kenya were relying on Mali and Cameroon to beat Angola and Benin respectively.
However, Benin managed to squeeze a barren draw against the Indomitable Lions, meaning they will now qualify for the knockout stages at the expense of Kenya.
The result also means Cameroon finished second in Group F to set up an interesting encounter with Nigeria in the Round of 16. Benin must wait to find out their next opponents.
Harambee Stars had started their campaign on a losing note by going down 2-0 to Algeria before recovering to beat East African neighbours Tanzania 3-2.
Then Senegal's damage to Kenya's goal difference placed the latter team in a poor position, behind South Africa and Benin who also have three points from three games.
