Ekitike was in tears when carried off the pitch on a stretcher at Anfield in the first half of Liverpool's 2-0 second leg defeat on Tuesday.
"Hugo suffered a serious injury against PSG on Tuesday night," France national team manager Didier Deschamps reported on Wednesday.
"Unfortunately, the severity of his injury will prevent him from finishing the season with Liverpool and from taking part in the World Cup."
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 international goals in eight appearances.
The 23-year-old made his France debut in September against Ukraine and scored his first goal against the same opponents in a 4-0 win in November which secured his country's place at the World Cup.
"Hugo is one of around 10 young players who made their debut for the national team in recent months," Deschamps added.
"He had settled into the squad perfectly, both on and off the pitch. This injury is a huge blow for him, of course, but also for the France team. His disappointment is immense."
France take on Senegal, Iraq and Norway in Group I at the World Cup in the US, Mexico and Canada, with the tournament starting on June 11.
Ekitike's injury is also a huge blow for Liverpool, who went out of the Champions League 4-0 on aggregate, and are battling to hold onto fifth spot in the Premier League to secure their place in next season's competition. They are on 52 points, four ahead of Chelsea with six games remaining.
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