A knee injury will keep the 39-year-old Irishman out.
He said last night: "It was feeling really good at the weekend and I was thinking I might have pulled out a bit early.
"But it's gone from acute pain to persistent niggling pain and it seems the physios know a thing or two."
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Hide AdHarrington was at nearby Sunningdale in his role as a Royal and Ancient Club ambassador for a clinic with schoolchildren brought together by the Golf Foundation charity.
He was also attending the European Tour's awards dinner at a Heathrow hotel and next up for him is the Formula One Monaco Grand Prix.
Harrington said: "I've never been to a grand prix, but I can't sit at home watching another tournament and I'm basically going to have a week's holiday to get me away from the temptation of practising."
He expects to start that again in the middle of next week on a trip to Sandwich, venue for this July's Open Championship, while his next tournament is in Memphis on 9-12 June, a week before the US Open.