Clarke was injured while practicing on the Doha Golf Club range after the pro-am on Tuesday.
The Northern Irishman arrived at the course on Wednesday hoping to start, but after hitting a few balls on the practice putting green Clarke advised officials he was not fit to play.
Clarke, who was set to become the 25th player to compete in 500 tour events, headed back to his hotel and a flight home.
''It's disappointing Darren's had to withdraw as the tour was looking forward to honoring his 500th tournament with a presentation before he teed off this morning,'' tournament director David Probyn said.
''We will just have to wait now until Darren next competes in a European Tour event.''
That will be the Masters at Augusta National from April 10, with Clarke taking up the third year of a five-year exemption in capturing the 2011 British Open.
He's next entered in the PGA Tour's Northern Trust Open from Feb. 13 in Los Angeles.