The Brazilian playmaker underwent a scan on Monday after suffering the blow during the Reds' 2-0 victory over Sunderland at Anfield on Saturday.
Ahead of Liverpool's EFL Cup clash against Leeds United, Klopp told BBC Sport: "Phil needs between five and a few weeks until we have him back. We will see. He is not in for tonight and for the next few games."
Coutinho, who has scored six goals in all competitions so far this season, has helped the Reds to second in the Premier League table after 13 games.