The Tottenham defender suffered a blow to the face in his club's 1-0 Premier League defeat to Newcastle United on Sunday.
When asked about Chiriches' injury after the game, Tottenham manager Andre Villas-Boas said: "I think he broke his nose."
The Romanian Football Federation confirmed in a statement that Chiriches, who boasts 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.
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.
‘Parma viewed him as the perfect replacement for Adrian Mutu, who’d left to sign for Chelsea. But Manchester United’s interest was much more concrete’: Cristiano Ronaldo's 2003 transfer details revealed by former Sporting director of football
'My shot was so clearly over the line – like Lampard against Germany. I was more gutted for my mates, as they’d backed me as the first goalscorer!’: England star reflects on agony of not being awarded maiden Three Lions goal
