Clarke pulled a hamstring more than a week ago while on holiday on the Bahamian island of Abaco and will miss the season's first major championship, which gets under way on Thursday.
"It is with deep regret that I will not be able to play at Augusta this year," Clarke said 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 pulled out of last week's Valero Texas Open in the hope that further rest would speed his recovery, but intensive treatment twice a day failed to have the required results.
The 44-year-old Northern Irishman, who missed the cut at Augusta last year on his first appearance since 2007, has yet to set a date for his return to action.
Clarke later explained how the injury occurred, adding: "I was playing tennis with the kids about two weeks ago and that is when I picked up the tear on my hamstring. It was just one of those freak injuries which is really disappointing.
"I have done absolutely everything to be at Augusta; physio, ultrasound and icing, but I cannot physically turn through shots and there is no point in going to the Masters if you are not one 100 per cent fit.
"Understandably, I am absolutely gutted not to be there but I hope to be fit enough to be back in action in the Ballantine's Championship on the European Tour in a couple of weeks' time."