Mane suffered the injury in Bayern Munich's recent Bundesliga game against Werder Bremen, with his participation at the Mundiale placed in doubt.
He was nonetheless named in manager Aliou Cisse's final 26-man squad for Qatar 2022 but will miss Senegal's opening games at the tournament, according to the Teranga Lions' Football Federation board member Abdoulaye Sow.
Sow stated: "Senegal will have to cope without its best player for the start of the tournament and not whine too much.
"We will have to rely on playing the first games without Sadio and win without Sadio because we have 25 players apart from Sadio.
"No one would have wanted it, but that's what's happened to us."
Mane's injury will see him miss the chance to face former Liverpool teammate Virgil Van Dijk when Senegal lock horns with Netherlands in their opening game on Monday.
Van Dijk missed last summer's European Championships with a serious knee injury and has sympathised with his former colleague.
"I don't think he will play [against the Netherlands]," Van Dijk told reporters. "I was feeling sad for him, first and foremost. I'm not happy in this case as I've been in that situation where I missed the Euros.
"We as players work so hard to get to this stage, and he has been such an important figure in that group for their country.
"I know for a fact that he will put a brave face on it, but it's tough and I feel sorry for him."
Senegal will also face hosts Qatar and Ecuador in Group A.
