"A regular CAS arbitration has been initiated and no procedural calendar has been fixed yet," the court said in a statement.
Cape Verde was the potential feel-good story of African qualifying, as the tiny islands appeared to have won its group.
However, Tunisia formally complained to FIFA that defender Fernando Varela had not completed a four-match ban for being sent off in a qualifier against Equatorial Guinea in March.
That match was also forfeited, by Equatorial Guinea, over an ineligible player but FIFA rules required that red and yellow cards stay on the record.
Cape Verde was stripped of the win and its playoff place, and fined 6,000 Swiss francs ($6,700) by FIFA.
FIFA's appeals committee upheld the ruling this month.