Mane suffered the injury while playing for Senegal against Sudan during the international break, and has been pictured in hospital with his hand in a cast.
This comes as more bad news for 'Reds' manager Jurgen Klopp, with both Virgil van Dijk and Mohamed Salah being sent home for medical attention this week.
Senegal did win the game 3-0 against Sudan, in what was a qualifier for the 2019 Africa Cup of Nations.
James Milner also underwent a hamstring injury against Manchester City last time out, meaning Klopp could face a selection dilemma ahead of Saturday's game at Huddersfield.