VAIL, Colo. — Lindsey Vonn will miss the Sochi Olympics because of a right knee injury, leaving the Winter Games without one of its biggest stars.

The 29-year-old skier from Vail, Colo., announced her decision Tuesday, exactly one month before the opening ceremony in Russia. Her personal publicist, Lewis Kay, said in a statement Vonn will have surgery “shortly.” Vonn grew up in Minnesota and learned to ski at Buck Hill in Burnsville.

In a Facebook posting, Vonn said she is “devastated” to miss the Olympics, “but the reality has sunk in that my knee is just too unstable to compete at this level.”

She took home two medals from the 2010 Vancouver Games, including becoming the first American woman to win an Olympic gold in the downhill. Vonn is also a four-time overall World Cup champion, the most recognized name in Alpine skiing — and, as it happens, the girlfriend of Tiger Woods.

Add it all up, and she would have been the focus of plenty of media coverage in Sochi, and certainly a main character in NBC’s coverage for a U.S. audience.

But Vonn tore two ligaments in her right knee during a high-speed crash at the world championships last February, sidelining her for about 10 months. She re-tore her surgically repaired ACL in a training crash in November, a key setback. Then, after returning to competition in early December by finishing 40th, 11th and fifth in a set of World Cup races at Lake Louise, Alberta, Vonn sprained her MCL during a race at Val d’Isere, France, last month.

“I did everything I possibly could to somehow get strong enough to overcome having no ACL,” Vonn said Tuesday via Facebook.

“I’m having surgery soon so that I can be ready for the World Championships at home in Vail next February,” she wrote. “On a positive note, this means there will be an additional spot so that one of my teammates can go for gold. Thank you all so much for all of the love and support. I will be cheering for all of the Olympians and especially team USA!”

Mikaela Shiffrin, the reigning world champion in slalom, and Julia Mancuso, a three-time Olympic medalist, will now draw extra attention as the most-accomplished American women trying to reach the Alpine skiing podium in Sochi.

Shiffrin, the U.S. teenager who has been labeled the “next Vonn” by some, wrote on Twitter that it’s “hard to swallow” that Vonn won’t be competing in Sochi. She added she’s “incredibly impressed” by Vonn’s determination.

Another American ski racer, Stacey Cook, posted on Facebook: “Bummed Lindsey Vonn. Our team is not the same without you. You leave big shoes to fill for the rest of the year.”

Vonn’s father, Alan Kildow, said in a telephone interview Tuesday: “She’ll come back. She’s come back. She’ll be back. You’ll see a lot of Lindsey Vonn in the future.”

After skiing in two downhills and a super-G at Lake Louise, Vonn sounded optimistic, declaring she would be in Sochi, “fighting for my medal.”

But a couple of weeks later in France, during a downhill — with Woods watching in the finish area — Vonn lost her balance, sending her left ski into the air, and forcing all her weight onto her right knee. She grimaced as she pulled up, then clutched that right knee.

Kay said Tuesday that an MRI after that episode “showed an MCL sprain, which coupled with the torn ACL, has made it impossible to stabilize her knee and be ready to safely ski again next month.”

Vonn’s motivation for a return, after the first procedure on her knee, clearly was Sochi. She was always a step ahead of schedule in her rehab, returning to snow about a month earlier than expected.

Now, she says her incentive is to be ready for the 2015 world championships in Colorado. There’s also this: Vonn needs three wins to match the World Cup record of 62 race victories set by Annemarie Moser-Proell of Austria.

“In looking ahead, I have every ounce of confidence that Lindsey will be in the starting gate next World Cup season, ready to compete,” said Bill Marolt, the CEO and president of the U.S. Ski and Snowboard Association who will step down shortly after the Sochi Games. “She knows the hard work it takes to get to the top and still has significant goals to achieve in what has been an incredible career.”

The American Alpine skiers captured eight medals four years ago, their highest total at any Olympics and twice as many as any other country at Vancouver. That figure may be tough to reach with Vonn sidelined and Bode Miller, who won three medals in 2010, trying to return to form after sitting out all of last season while recovering from a left knee injury.

What’s more, Mancuso has been struggling this season. Off to a poor start in pre-Olympic races, Mancuso recently headed home for a short break.

“We have a strong team that is well prepared. … Now is the time for those athletes to step up,” Marolt said.