The British rider had to surrender his defence of the prestigious road race title after falling on Tuesday's fourth stage and twice more in Wednesday's wet conditions.
He flew back to his South of France headquarters later that night to undergo medical checks and scans have since revealed the extent of the damage suffered by the Team Sky cyclist.
He tweeted on Friday evening: "MRIs done, confirmed fractures to the left wrist & right hand. Time for some R&R..."
Froome, 29, may target September's Tour of Britain to make his return.