The Romanian international picked up the injury two weeks ago during a game of beach football.
Scans have shown that Chivu has broken a metatarsal in his right foot and he is likely to be out of action for several weeks.
The former Ajax star will be unable to take part in Roma's pre-season training camp in Austria although he is still expected to travel with his team-mates.
Roma will hope that Chivu can make a speedy recovery as they will want him fit for the start of the new season having lost Walter Samuel to Real Madrid.
