The 23-year-old pointed to his Achilles tendon as medical staff attended to him before he was carried off on a stretcher at Anfield, where Liverpool lost 2-0 in their quarter-final second leg, exiting the competition with a 4-0 aggregate defeat.
The French football federation (FFF) was not immediately available for comment.
Ekitike has 17 goals in all competitions this season since Liverpool signed him from Frankfurt for £69 million in July, and has scored twice for France since the start of the current campaign.