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The 32-year-old, who finished in a tie for 13th at the Travelers Championship on Sunday, said in a statement: "I'm disappointed to withdraw from the AT&T National, but the last three weeks have been extremely demanding both mentally and physically."
Rose, who won the 2010 tournament around Congressional Country Club, added: "This tournament has been very good to me - especially in 2010 - and I would play if I felt I could. Tiger and his Foundation run a great tournament, and I wish I could be there."
He later admitted on Twitter that he felt he had "hit the wall" after his closing round of 71 at the TPC River Highlands, in Connecticut.
World number one Tiger Woods had already withdrawn from the tournament after suffering an elbow injury at the US Open at Merion.
Rose has not yet signalled if he will pull on his golf clothing before next month's Open Championship at Muirfield.
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