The 23-year-old was forced off during the first half of Liverpool's Champions League quarter-final second leg against Paris Saint-Germain at Anfield on Tuesday after slipping on the turf. Liverpool lost 2-0 to exit 4-0 on aggregate.
Scans have since confirmed the severity of the forward's injury, with Liverpool saying Ekitike will be sidelined for the remaining weeks of the campaign.
The injury will also rule him out of this year's World Cup, the club added, after France manager Didier Deschamps said on Wednesday the striker would miss the finals in North America.
"Further updates will be provided at the appropriate time, with Hugo receiving the full support of everyone at LFC," Liverpool said in a statement.
Ekitike joined Liverpool in July from Eintracht Frankfurt and is their top scorer this season with 17 goals in all competitions, including 11 in the Premier League. He has netted two goals for France in eight appearances.