The 17-year-old left the field after he was caught on his ankle by a Gibraltar defender while scoring in France's 14-0 win.
Zaïre-Emery became France's youngest player since 1914 and also the youngest goal scorer for the country since that date in the Euro 2024 qualifier.
"Warren Zaïre-Emery has suffered a moderate sprain of his right ankle and will remain under treatment until the winter break," PSG said in a statement.
Zaïre-Emery will miss France's last Euro qualifier against Greece on Tuesday. He will also be unavailable for PSG's next five Ligue 1 fixtures and final two Champions League group games.