The 2011 Open champion suffered the blow on holiday a week ago, missing the Valero Open in Texas last week, and has not recovered in time for the season's first Major.
"It is with deep regret that I will not be able to play at Augusta this year," said Clarke on his official website. "Playing in The Masters is one of golf’s greatest pleasures and I am very disappointed to be missing out."
Clarke, who won his only major title at the 2011 British Open after holding off Americans Phil Mickelson and Dustin Johnson, was also forced to withdraw from last week's Texas Open on the U.S. PGA Tour because of the injury.
Despite having rest and extensive treatment on his hamstring, Clarke felt he would not be able to cope at the Masters with the challenge of competing on the notoriously hilly terrain at Augusta National.
The Northern Irishman, whose best finish at the Masters was joint eighth on his tournament debut in 1998, said he will continue having treatment on his hamstring in the Bahamas and no date has been set for his return to golf.
Clarke will not be replaced in the field for the 2013 Masters, which starts on Thursday.