The 6ft 5in (1.96m) centre-back injured his left ankle during Sunday's Group C opener in Cairo and will miss "between 10 and 15 days" with a sprained ligament, the Senegalese FA said Monday.
Sane, who was expected to partner Napoli standout Kalidou Koulibaly in a strong Senegalese defence, will miss Thursday's heavyweight clash with Algeria as well as the July 1 meeting with Kenya.
Senegal will however be boosted by the return of star forward Sadio Mane, who was suspended for the opener after picking up a one-match ban during qualifying.
Koulibaly, reportedly coveted by a number of Europe's top sides, said Sunday he wasn't prepared to talk about his Napoli future with Senegal attempting to win the tournament for the first time.
"I'm not talking about my future, I would rather talk about Senegal. We know that Senegal want to do something great," said Koulibaly.
"I'm 200% with Senegal, I'm 200% with the 15 million Senegalese. So today I'm relaxed, I'm going to play my AFCON and then go back to Naples, and we'll see what happens."