Ledley, while on a short holiday in Paris, stumbled and took the weight of the fall on his wrist leaving himself with a cracked bone.
"If the referee gives the go-ahead for Joe to play against Russia on Wednesday, as we hope, then he'll be fit to play for Cardiff City next Sunday," said chairman Peter Ridsdale.
Joe is on international duty along with David Marshall, Gavin Rae (both Scotland), Gabor Gyepes (Hungary) and Josh Magennis (Northern Ireland U21's).
