Chiriches is set to undergo surgery Monday but the club did not give an estimate for how long his recovery was expected to take.
Napoli was drawn in Group C, alongside Paris Saint-Germain, Liverpool and Red Star Belgrade.
Chiriches's injury leaves Napoli's Italian coach Carlo Ancelotti with only three experienced central defenders available, including Spain international Raul Albiol, Senegal international Kalidou Koulibaly and Serbia international Nikola Maksimovic.
Ancelotti also has the option of tapping Italian 22-year-old Sebastiano Luperto, who made the first team after moving up through the youth ranks.
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