The English world number three, who eight days ago triumphed by two shots in the 113th Open at Merion Golf Club, tied for 13th at the Travelers Championship on Sunday in his very next tournament appearance.
Rose felt obliged to fulfill his playing commitment at the Travelers in Cromwell, Connecticut, despite a hectic start to last week which involved a whirlwind media tour in New York City where he appeared on several talk shows.
"I'm disappointed to withdraw from the AT&T National, but the last three weeks have been extremely demanding both mentally and physically," Rose said in a statement issued by the US Tour on Monday.
"This tournament has been very good to me - especially in 2010 - and I would play if I felt I could. Tiger (Woods) and his Foundation run a great tournament, and I wish I could be there."
Rose, who won the AT&T National in 2010 when it was held at Aronimink, has been replaced in the field at Congressional by American Brendon Todd.
The AT&T National, being played in Bethesda, Maryland from June 27-30, is already missing world number one Woods, who withdrew last week after being diagnosed with a left elbow strain.
Woods, who won last year's AT&T National to move past Jack Nicklaus into second place on the all-time US Tour winners' list, does not expect to return to competition until next month's British Open at Muirfield in Scotland.
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