The last team to achieve the feat, South Africa, went on to win the 1996 tournament by defeating Tunisia 2-0 in the final in Soweto.
Here, AFP Sport lists 10 things to know about the Indian Ocean island team that shocked three-time champions Nigeria 2-0 in the group stage.
-- They are relatively old with eight of the 23-man squad 30 or over and there are no teenagers. Defender Jeremy Morel, 35, is the oldest and midfielder Rayan Raveloson, 22, the youngest.
-- The players are with clubs in France (10), Reunion (three), Algeria, Belgium, Bulgaria, Egypt, Saudi Arabia, South Africa, Thailand and the United States (one each) plus two locals.
-- Goalkeeper Jean Randrianasolo from champions CNaPS Sport and midfielder Jean Rakotoarisoa of Fosa Juniors are the pair who play on the vast island.
-- Malagasys have the longest surnames in African football, and the list is topped by Saudi Arabia-based forward Charles Andriamahitsinoro with 17 letters.
-- The captain is forward Faneva Andriatsima, a 35-year-old who plays for French second-tier outfit Clermont Foot.
-- They are ranked 108 in the world with the Faroe Islands one place higher and Zimbabwe next in the list. Quarter-final opponents Tunisia are ranked 25th.
-- The team nickname is Barea, prized cattle with long horns who signify wealth in one of the poorest countries in the world.
-- Madagascar play at the rudimentary Stade Mahamasina, a 22,000-capacity ground in the capital, Antananarivo, used predominantly for football and rugby union fixtures.
-- The closest the Barea previously came to qualifying was for the 1984 finals in the Ivory Coast -- they lost 2-1 on aggregate to Malawi in a final round eliminator.
-- Despite starring in Egypt, Madagascar are only among the third seeds for the 2021 Cup of Nations qualifying draw to be made next Thursday in Cairo.