Al-Faraj was injured at the end of the first half of the historic 2-1 victory over Argentina in Saudi Arabia's first match in the tournament.
He left the stadium on crutches, with an apparent leg injury, and Renard said he did not expect him to participate in any more matches.
"Herve Renard has given team captain Salman Al-Faraj his permission to officially leave the Green Falcons' camp following the medical team's assessment that he will no longer be fit to play," the national federation said in a statement on Twitter.
Saudi Arabia, who lost 2-0 to Poland on Saturday, are equal with Argentina on three points, while Poland tops the group with four and Mexico lasts with one point.
Saudi Arabia needs to beat Mexico in the last match in the group to ensure qualification for the last 16, regardless of the outcome of the match between Poland and Argentina.