Kompany's appearances has been limited due to injury this season and has only featured in 10 Premier League contests, last having played against Burnley on 3 February.
It has been an even longer time coming in Europe for the Belgian defender, who has not played in the Champions League since the May 2016 semi-final against Real Madrid.
He is joined in defence by Kyle Walker and the returning Fabian Delph, with Nicolas Otamendi preferred over John Stones and Aymeric Laporte by Pep Guardiola.
It is no surprise Sergio Aguero and Kevin De Bruyne keep their places fresh off four-goal and three assist performances against Leicester City last weekend, respectively. However, Bernardo Silva comes into the team for David Silva, who started City's 5-1 win over Leicester City but drops to the bench in Basel.
Also of note on the bench is Leroy Sane, who has made the team despite initially be diagnosed with a six-to-seven week injury. Guardiola admitted to being surprised at the Germany international's quick return on Monday and has rewarded him with a place on the 18.
Manchester City XI: Ederson; Walker, Kompany (C), Otamendi, Delph; Fernandinho, Gündogan, De Bruyne, Sterling, Bernardo; Agüero
Subs: Bravo, Danilo, Stones, Laporte, Sané, Silva, Foden
Basel XI: Vaclik; Lacroix, Xhaka, Suchy; Lang, Frei, Serey Die, Riveros; Elyounoussi, Stocker; Oberlin
Subs: Salvi, Petretta, Zuffi, Van Wolfswinkel, Ajeti, Manzambi, Bua