The Napoli centre back, who has 43 caps, would return to Rome for further treatment, the FRF said in a statement.
The former Tottenham Hotspur defender's injury is a big blow for German coach Christoph Daum, who will take charge of Romania for the first time in Sunday's match in Cluj after replacing Anghel Iordanescu in July.
The absence of Chiriches may open the door for Ludogorets centre back Cosmim Moti, the 31-year-old emerging as favourite to partner Dragos Grigore in the heart of the Romania defence.
Romania are in UEFA World Cup qualifying Group E, along with Denmark, Poland, Armenia, Montenegro and Kazakhstan.
(Reporting by Angel Krasimirov; Editing by John O'Brien)
