Adler, one of several goalkeepers battling for a position as understudy to Manuel Neuer in the German national side, sat out Hamburg's last two Bundesliga games before the winter break with the injury.
"I've tried everything to be fit again as quickly as possible," Adler told Hamburg's website (www.hsv.de).
"We thought that it would be fine after the 10 day (Christmas) break, but it got worse during the very first training session."
Hamburg said that Adler would fly home from Abu Dhabi, the second stop on their winter getaway after Indonesia, for further examination and treatment.
Adler, Marc-Andre ter Stegen and Ron-Robert Zieler in the mix for the two reserve positions in Germany's World Cup squad behind Neuer, the undisputed first choice.
Adler missed the 2010 World Cup after suffering a broken rib before the tournament. He was Germany's number one goalkeeper at the time and Neuer has never looked back since taking his place in South Africa.