Skrela managed just 11 minutes after coming on as a second-half replacement in the 47-21 victory over Japan on Saturday after being left in a heap following a collision.
"We decided yesterday evening that David could no longer be competitive for us following his injury on Saturday," Lievremont told reporters on Wednesday.
"Having thought about it for a few days, seeing how it evolved and consulting certain French experts as to the nature of the injury, we have had confirmation that it will require a certain number of weeks recovery."
Skrela will be replaced in the squad by uncapped Jean-Marc Doussain of Toulouse.
"I am obviously hugely disappointed. it's been two months since I've been preparing for this competition. It's one of the hazards of sport." Skrela bemoaned.
France play Canada in Napier on Sunday before finishing their Pool A campaign against hosts and tournament favourites New Zealand and Tonga.