The Tottenham centre-back withdrew from Sunday's Premier League defeat by Newcastle with a suspected broken nose and has been replaced by Dinamo Bucharest's Dragos Grigore
The Tottenham centre-half suffered a blow to the face in his club's 1-0 Premier League defeat to Newcastle on Sunday.
When asked about Chiriches's 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 on Monday that the former Steaua Bucharest man, who has 22 caps to his name, 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 play the away leg of their tie with Greece in Piraeus on Friday, with the return match taking place in Bucharest four days later.