Ancelotti will return to Italy for the funeral, which takes place on Saturday, before returning to England, and the dug-out, for Sunday's game.
A statement on Chelsea's official website read: "Carlo Ancelotti's father Giuseppe passed away in Italy last night aged 87 with his son at his side. 'Everyone at Chelsea Football Club sends our deepest condolences to Carlo and his family. They are all in our thoughts at this time.
"The funeral will take place in Italy on Saturday. Carlo will return to London for Sunday's match versus Arsenal."