The 33-year-old had to be carried off the pitch in the first half of Denmark's 1-0 win against Peru on Saturday after being injured in a challenge with Peru's Jefferson Farfan and was replaced by Lasse Schone, reported Xinhua news agency.
"William Kvist has suffered a rib injury and is travelling home to Denmark. Everyone around the team wishes him a good recovery," said the Danish FA on its 'Twitter' account.
A hard-working holding midfielder, Kvist may not have been the most technical player in the Denmark side, but his 84 caps show his enormous importance to the team. And it will be interesting to see who replaces him against Australia in Denmark's next group game, where a win for the Danes would almost certainly book their place in the last 16 of the tournament.