The defender was released from the France squad on Friday and returned to Merseyside.
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Posting on their officials website, Liverpool said: "Ibrahima Konate will not take part in France’s match against Iceland on Monday.
"The centre-back missed Les Bleus’ win over Azerbaijan on Friday and it has now been announced that he is not available for their next match in Reykjavik."
A statement from the France national team read: “Injured in the right quadriceps during his last match with Liverpool, Ibrahima Konate has followed a treatment and protocol since his arrival this Monday but will not be able to take his place against Iceland.”