They were the first two countries to emerge from the draw in Cairo, soliciting gasps from the small audience at the Confederation of African Football's headquarters.
The other four ties will see Ethiopia play Nigeria, Tunisia meet Cameroon, Ghana take on Egypt and Burkina Faso against Algeria.
Senegal have been banned from using their stadium in Dakar since rioting brought a premature halt to the African Nations Cup qualifier against Ivory Coast in October.
The match was stopped 14 minutes from the end as frustrated home supporters lit fires on the terraces and threw objects on to the field after Didier Drogba's penalty had put the Ivorians in control of the two-legged tie.
Senegal have undergone a major overhaul since their Nations Cup elimination, appointing former France World Cup midfielder Alain Giresse as coach and dumping top players like Demba Ba of Chelsea.
They won their World Cup group despite hosting qualifiers in neutral Guinea and Morocco and will have completed their ban by the time they host the second leg of the playoff against Ivory Coast.
However, it has not yet been decided if they will take the match to the same Leopold Senghor Stadium where last year's riot occurred.
World soccer's ruling body FIFA has asked the 10 playoff countries to nominate the day of the ties, venues and kickoffs by Friday.
The first legs must be played between Oct. 11-15 and the return games between Nov. 15-19. The winners qualify for the World Cup in Brazil.
Burkina Faso and Ethiopia are looking to reach the finals for the first time.
Ethiopia have a tough assignment against Nigeria while Burkina Faso will fancy their chances against mercurial Algeria who are ranked third in Africa despite having had a poor Nations Cup in South Africa at the start of the year.