The first game Mane will sit out is Manchester United's visit to Anfield on Saturday afternoon.
The Reds forward suffered a hamstring injury while away on global duty this week.
The forward sustained the grade-two injury on worldwide duty with Senegal on Saturday and could be absent for 10 matches. But Mane missed the end of Liverpool's last campaign with a knee injury and was also away in January for the Africa Cup of Nations.
"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".
Iran end group stage in style
The problem for Costa Rica is that they are playing against Iran - a team that has surpassed and shocked most in Goa. Iran coach Abbas Chamanian lauded his defence for their excellent work rate through all three group games.
The 25-year-old's importance to Liverpool going forward is unquestioned. That brought them only four goals across a 1-1 Premier League draw with Burnley and back-to-back meetings with Leicester City, who knocked Liverpool out of the Carabao Cup before the Reds responded with a 3-2 league win.
Since signing for Liverpool from Southampton for a fee of £34 million in 2015, Mane has been in excellent form and has left a gaping hole in the side whenever he has not been available for selection.
Mane has scored three goals in five Premier League appearances this season and has just returned from a three-match suspension.
Philippe Coutinho's return to the first-team setup after the transfer window closed saw midfielder Georginio Wijnaldum drop to the bench for Liverpool, with Klopp fielding a front three of Mane, Roberto Firmino and Mohamed Salah.