The 25-year-old picked up the injury in the latter stages of Senegal's 2-0 win over the Cape Verde Islands on Saturday.
"Sadio Mane is facing a spell on the sidelines after sustaining a hamstring injury on international duty, Liverpool FC can confirm," read a statement on the club's official website.
"The winger was substituted 89 minutes into Senegal's 2-0 World Cup qualifying win over the Cape Verde Islands on Saturday. And it has now been confirmed that he picked up an injury during that fixture that could keep him out of action for up to six weeks."
Mane has scored three Premier League goals in four appearances for the Reds at the start of the 2017-18 campaign.