Ghana failed to overturn a 1-0 first leg deficit against Burkina Faso, drawing the second leg 0-0 in Ouagadougou.
It means the Black Stars will not play at the CHAN - a competition restricted to African footballers who play in their country of birth - for a third consecutive time.
Senegal, recent winners over Ghana in the final of the Wafu Cup of Nations, were also big name casualties, going out to Guinea on penalties.
Senegal went to Conakry with a 1-0 advantage but Guinea fought back to win their home leg 1-0 courtesy of a Mamadouba Bangoura goal.
With the tie level at 1-1, the hosts went on to win the ensuing penalty shootout 3-1.
Ivory Coast also failed to qualify for the finals despite winning their home leg against Niger 1-0. The Elephants' 2-0 defeat away to Niger in the first leg meant they lost the tie 2-1 on aggregate.
Also on Sunday, Zimbabwe booked their place at Cameroon 2020 with a 0-0 draw in Lesotho to go through 3-1 aggregate.
DR Congo beat Central African Republic 4-1 in Kinshasa to progress 6-1 overall and Congo Brazzaville also qualified with a 1-0 home win over Equatorial Guinea to win 3-2 overall.
In the north zone, Tunisia booked their place with a 3-1 aggregate win over Libya.
Mali will also play at the finals in Cameroon, defeating Mauritania 2-0 overall.
Nigeria were the big casualties on Saturday, losing out to Togo as holders Morocco went through with victory over Algeria.
Qualified Teams for 2020 African Nations Championship (CHAN) in Cameroon:
Cameroon (hosts) Tanzania Uganda Rwanda Zambia Namibia Togo Morocco Zimbabwe DR Congo Congo Tunisia Burkina Faso Guinea Niger Mali