Mane played in Senegal's World Cup qualifying win over Cape Verde on Saturday, but was substituted in the closing stages of the game after picking up the problem.
A statement on the Reds website reads: "Sadio Mane is facing a spell on the sidelines after sustaining a hamstring injury on worldwide duty, Liverpool FC can confirm".
Liverpool won just once in seven matches in all competitions while Mane was at the African Nations Cup in January.
The 25-year-old - who has three goals in five Premier League games - has only been involved in one domestic match since returning from that suspension, and now looks set for an even longer absence.
They have already had to cope without Mane for some of this season, domestically at least, after his red card against Manchester City led to a three-match ban.
Since his debut in August 2016 Liverpool average 2.2 Premier League goals with Mane in the team, compared to 1.6 goals in his absence.