The Tottenham center back withdrew from Sunday's loss to Newcastle with a suspected broken nose and has been replaced by Dinamo Bucharest's Dragos Grigore.
The Tottenham center back suffered a blow to the face in his club's 1-0 Premier League defeat to Newcastle on Sunday.
When asked about Chiriches' injury after the game, Spurs boss Andre Villas-Boas told the press: "I think he broke his nose."
The Romanian Football Federation confirmed in a statement Monday that the former Steaua Bucharest man, who has 22 caps, would not be fit to feature in either match against Greece.
Dinamo Bucharest's Dragos Grigore has been named as a replacement for the 23-year-old defender.
Romania plays the away leg of its playoff with Greece in Piraeus on Friday, with the return match taking place in Bucharest four days later.