Cilic had to pull out of the Rogers Cup in Montreal because of the problem and now he has decided to miss the upcoming Cincinnati Masters, where he would have been the defending champion, as he is still not 100 per cent fit.
The Croat has confirmed he is recovering well but he wants to make sure he's ready for the US Open at the end of the month so has decided against going to Cincinatti.
He said: "I have already started with my preparation and the progress is going well but there isn't enough time for me to prepare for Cincinnati and to be completely ready to play there. I still don't feel at 100 per cent to compete at the top level and to defend my title in Cincinnati."
The 28-year-old suffered the injury at Wimbledon, where he lost to Roger Federer in straight sets in the final.