Asensio underwent successful left knee surgery in Spain for a cartilage lesion and faces approximately three months of rehabilitation.
Ake suffered a moderate strain and swelling in his right leg during a match against Slavia Prague in the Champions League.
Fenerbahce played a 2-2 draw at home against the Czech side on Tuesday.
Ake underwent an MRI scan at Atasehir Medicana Hospital and is expected to miss approximately three weeks.