Senegal won Group B despite scoring only one goal in three games, while Cape Verde qualified after finishing third in Group A.
Morocco topped Group C and will be expected to advance to the quarter-finals at the expense of a Malawi side that was third in Group B and will be playing its first AFCON knockout match.
Senegal v Cape Verde 25/01 3am AEDT on beIN 1
This will be the first Africa Cup of Nations clash between the two nations and Cape Verde will be playing only their second ever knockout match in the tournament.
The Blue Sharks were beaten 2-0 by Ghana at the quarter-final stage in 2013 and they will have to defy the odds at Kouekong Stadium to reach last eight once again.
Cape Verde coach Pedro Brito believes his players can spring a big surprise in Bafoussam.
He said: "We have worked hard in our training and facing a team like Senegal is an added motivation, because the match is like a derby.
"They have to respect us as a team the same way we respect them.
"The competition has seen a lot of surprises, and we hope to be the other team that will cause an upset as our mission is to win the game and move to the next round."
The Lions of Teranga have not been firing on all cylinders, but they are the only side in the tournament not to have conceded a goal.
The three sides to have faced Senegal have only been able to muster three shots on target between them, so Cape Verde must grasp any chances it is able to create.
One to watch: Idrissa Gueye (Senegal)
Paris Saint-Germain midfielder Gueye is a key man for Senegal, getting through so much work in the middle of the park.
Gueye has played a big part in his side being so solid and the industrious former Everton man can boss the midfield battle.
Morocco v Malawi 25/01 6am AEDT on beIN 1
Malawi and Morocco will also lock horns for the first time in the AFCON at Stade Ahmadou Ahidjo.
Underdog Malawi will be playing only its 10th game in this competition and it has only won two Africa Cup of Nations matches.
It is unbeaten in two games, though, having remained in the tournament courtesy of a 2-1 win over Zimbabwe and a battling goalless draw against Senegal.
Morocco beat Ghana and Comoros en route to last 16 before a 2-2 draw with Gabon.
Vahid Halilhodzic's side will under pressure to progress in Yaounde by dispatching a Malawi side that had an average of just 31.5 per cent of possession in the group stage, the lowest of any team.
One to watch: Sofiane Boufal (Morocco)
Boufal is Morocco's leading scorer in the tournament with two and he also created 10 chances
Only Algeria’s Youcef Belaïli created more opportunities in the group stage with 12 and Morocco will expect the winger to step up again.