Stones is ill while Silva is struggling with a kick he took in the midweek win over West Brom.
Danilo also comes into the side for Oleksandr Zinchenko at left-back.
Aymeric Laporte, who made his debut against West Brom in midweek, will drop to the bench.
Guardiola has managed to name an unchanged forward line, however, with Sergio Aguero playing centrally, between Raheem Sterling and Bernardo Silva.
Man City starting XI: Ederson, Walker, Kompany, Otamendi, Danilo, Fernandinho, Gundogan, De Bruyne, Bernardo, Aguero, Sterling
Subs: Bravo, Laporte, Adarabioyo, Zinchenko, Yaya Toure, Diaz
Burnley starting XI: Pope; Bardsley, Long, Mee, Taylor; Cork, Hendrick; Lennon, Barnes, Gudmundsson; Vokes
Subs: Lowton, Nkoudou, Arfield, O'Neil, Wells, Lindegaard, Westwood