Mane, 25, was substituted in the 89th minute of a 2-0 World Cup qualifying win over Cape Verde on Saturday.
He is set to miss Premier League games against Manchester United and Tottenham and both Champions League group fixtures against Maribor.
Mane has scored three goals in five league appearances so far this season.
Senegal, who are top of their World Cup qualifying group, face two crucial games against South Africa on 10 and 14 November, which Mane is also likely to miss.
He was suspended for three games earlier this season after being sent off in the 5-0 defeat at Manchester City, while he also missed the end of last term with a knee injury.
Liverpool won just once in seven matches in all competitions while Mane was at the African Nations Cup in January.
They average 2.2 Premier League goals with Mane in the team, compared to 1.6 goals in his absence.
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