The 30-year-old forward, whose decisive penalty kicks won both the Africa Cup of Nations and World Cup qualification for his country this year, suffered an injury to his right fibula in Bayern's 6-1 win against Werder Bremen and misses this weekend's clash against Schalke.
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But coach Aliou Cisse included the team's talisman when he named his 26-man squad at a news conference in Dakar on Friday, saying he was confident Mane could recover in time to play at the tournament.
He said Senegal had sent the Senegalese federation's doctor to examine Mane on Thursday and had been told he would not require surgery.
"That's very good news and we now have the chance to try and get him fit for the tournament. We now have two weeks to observe and see how the injury reacts to treatment," Cisse said.
"I prefer to keep him in the squad because he is such an important part of us."
The coach used the example of Watford forward Ismaila Sarr, who had been injured going into January's Africa Cup of Nations finals, but was included in the squad and recovered after the first round to contribute to Senegal's success in the tournament.
"We will do all in our power to ensure we can recover Mane in time to play," Cisse added.
In response to FIFA General Secretary Fatma Samoura's suggestion that Mane could be treated by "witch doctors" to get him fit in time, Bayern coach Julian Nagelsmann told a a news conference: "I don't even know what a witch doctor is.
"In 10 days we will do a check on him again to see how his recovery and progress has gone and we will take it from there. Obviously [Senegal] really want him to play but we have to wait and see how the medical situation is.
"If he can't play he can't play, whether the FA want him or not. "These are the types of situations that go beyond just the sporting aspect."
Cisse kept faith with the majority of the squad that won AFCON in Cameroon but did include defender Ismail Jakobs and strikers Nicolas Jackson and Ilimane Ndiaye, who earned their first caps after World Cup qualification was secured in March.
"The players chosen correspond with our vision and philosophy. They are competitors of a high level," said Cisse, who had his contract as coach extended by a further two years on Thursday.
Senegal squad in full:
Defenders: Fode Ballo-Toure (AC Milan), Pape Abou Cisse (Olympiakos), Abdou Diallo (RB Leipzig), Ismail Jakobs (Monaco), Kalidou Koulibaly (Chelsea), Formose Mendy (Amiens), Youssouf Sabaly (Real Betis)
Midfielders: Pathe Ismael Ciss (Rayo Vallecano) Krepin Diatta (Monaco), Idrissa Gana Gueye (Everton), Pape Gueye (Marseille), Cheikhou Kouyate (Nottingham Forest), Mamadou Loum (Reading), Nampalys Mendy (Leicester City), Moustapha Name (Pafos FC), Pape Matar Sarr (Tottenham Hotspur)
Forwards: Boulaye Dia (Salernitana), Famara Diedhiou (Alanyaspor), Bamba Dieng (Marseille), Nicolas Jackson (Villarreal), Sadio Mane (Bayern Munich), Ilimane Ndiaye (Sheffield United), Ismaila Sarr (Watford).