Justin Rose waves after putting on the 18th hole to complete the final round and win the 113th U.S. Open at Merion Golf Club on June 16. (Ross Kinnaird/GETTY IMAGES)

Less than a week after losing Tiger Woods to injury, the AT&T National suffered another marquee withdrawal Monday. Justin Rose, who earlier this month staved off Phil Mickelson to win the U.S. Open, cited the toll it took to notch the most significant victory of his career in saying he, too, would bypass Washington’s annual PGA Tour stop.

“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. “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.”

Thus, a tournament that two weeks ago boasted a field that was likely to include three of the top four players in the world golf rankings now has but one remaining — Masters champion Adam Scott. Woods, the world’s top-ranked player whose foundation both organizes and benefits from the tournament, withdrew Wednesday because of a strained left elbow that bothered him as he struggled at the U.S. Open, which Rose won June 16 at Merion Golf Club outside Philadelphia.

Rose will be replaced in the field by alternate Brendon Todd, a 27-year-old Georgia grad who splits his time between the PGA and Web.com tours.

The AT&T National, which runs Thursday through Sunday at Bethesda’s Congressional Country Club, will now include just three of the top 20 players in the world – Scott, the popular Australian ranked fourth; American Brandt Snedeker, the Fed­Ex Cup winner ranked eighth; and Jason Day, the 25-year-old Australian who tied with Mickelson at Merion, two shots behind Rose.

It isn’t unusual for winners of major championships to alter their schedules following those victories. The day after winning at Merion, Rose went on a media blitz in New York, appearing on the “Today” show, bringing his trophy to the floor of the New York Stock Exchange and delivering the top 10 list on “The Late Show with David Letterman.”

Still, he kept his commitment to the Travelers Championship outside Hartford, and he even opened the tournament with rounds of 67, 68 and 68 to get on the fringes of contention. But he hit a poor approach shot at the ninth on Sunday for his first bogey of the day and never contended from that point, finishing tied for 13th.

“I think I was just a little clumsy today when I needed to be sharp,” Rose told reporters afterward. “I think the proof’s in the pudding, you know. Getting to 9 under and having a chance and not being able to kind of finish it out cleanly, I think that probably shows more fatigue than anything.”

Rose, who won the 2010 AT&T National when it was played at Aronimink Golf Club outside Philadelphia, had reaffirmed his commitment to Congressional last week. He now has three weeks off before the British Open begins July 18 at Muirfield in Scotland.

The AT&T National, though, continues to struggle drawing marquee fields — partly because of coincidence and partly because of its spot on the calendar. Rose, who lives most of the year in Orlando, is one of the few European players who doesn’t head back across the Atlantic after the U.S. Open. Rory McIlroy, for instance, would seem a natural for Congressional’s event, given he won the U.S. Open there in 2011. But McIlroy, ranked second in the world, has played in the Irish Open, the European Tour event that coincides with the AT&T National, the past two years.

Woods’s withdrawal, though, has the most impact. Though Woods expects to be ready at Muirfield, his presence can change the feeling of an entire field, raising both attendance and television ratings. Woods is due to be at Congressional on Wednesday to participate in opening ceremonies and host a news conference, but he, like Rose, will watch the actual tournament from afar.