Woods, who had back surgery on March 31 and performed poorly in four tournaments after returning -- including a withdrawal during the final round of the Bridgestone Invitational -- had not been ruled out by Watson, who said Monday that Woods would be given time to assess his own medical situation and game.
"While I greatly appreciate Tom thinking about me for a possible captain's pick, I must take myself out of consideration," Woods said. "I've been told by my doctors and trainer that my back muscles need to be rehabilitated and healed. They've advised me not to play or practice now.
"I'm extremely disappointed that I won't be ready for the competition. The U.S. team and the Ryder Cup mean too much to me not to be able to give it my best. I'll be cheering for the U.S. team. I think we have an outstanding squad going into the matches."
Woods said on his website that he would not compete again until the World Challenge set for Dec. 4-7 at Isleworth in Orlando, the annual tournament that benefits his foundation and is moving to Florida from California.
That means Woods will skip an October team event in Argentina along with Matt Kuchar -- one where he was expected to receive a hefty appearance fee -- along with other corporate exhibitions in Asia in November, said Woods' agent Mark Steinberg.
"We all saw that he was in pain," Steinberg said. "To me, the good news is that the residual effect of him playing the last few weeks has been muscular and not directly related to the surgical procedure that was done.
"He's going to come back at the World Challenge and we'll take it from there. He needs this time to rest and rehabilitate."
Nine members of the U.S. Ryder Cup team became finalized on Sunday at the completion of the PGA Championship, with Watson getting three at-large picks, that he will make on Sept. 2.
The competition begins Sept. 26 at Gleneagles in Scotland.
Despite the back surgery to alleviate a pinched nerve, Woods all along has been said to be a candidate by Watson, who maintained Woods needed to be playing well and healthy.
After the Open Championship, Woods called Watson to express his desire to be on the team, and even the latest back issue that occurred at the Bridgestone Invitational and kept Woods from performing well at the PGA Championship didn't rule him out.
"I don't make this comment loosely," Watson said Monday. "He is Tiger Woods and he brings a lot to the team if he has the ability to play and he is healthy. He brings a lot to the team. And I would be a fool not to consider him."
Woods decided to end any drama about the picks now.
"My primary wish is for Tiger to be healthy and competitive, and I hope that he'll return to the game very soon," Watson said in a statement Wednesday. "Of course I'm disappointed that Tiger Woods has asked to not be considered for the U.S. Ryder Cup team, and that his health is not where he would like it to be.
"However, I think we can all agree that we need Tiger Woods in this great sport, and he has taken the high road by informing me early on in the selection process. My focus will be on identifying three players to join the U.S. team and give us the best chance for success at Gleneagles."
Jason Dufner, who withdrew from the PGA with a neck injury, Ryan Moore and Brendon Todd were next in the points standings. Both Moore and Todd missed opportunities to clinch a spot on the team with lackluster finishes at the PGA on Sunday.
Other candidates could be major champions Keegan Bradley and Webb Simpson, as well as Brandt Snedeker. All were on the 2012 team that lost to Europe 14½ to 13½.
Woods has played on seven U.S. Ryder Cup teams, just one of which was victorious -- the 1999 squad. He missed the 2008 victory due to his recovery from knee surgery. His overall record in the competition is 13-17-3, with a 4-1-2 singles record.
The fact that Woods has ruled himself out of competition for possibly three months suggests he has issues to deal with following his latest setback.
Woods said at the PGA Championship that the injury he suffered to his back on Aug. 3 was not related to the March 31 surgery, that he jarred it when falling awkwardly into a bunker, his back going into spasm for the rest of the round.
Through treatment and rehabilitation, Woods pronounced himself fit to play last Wednesday, only to show signs of distress during rounds of 74-74. On Friday, Woods said he suffered a recurrence while warming up on the driving range, but played through it.
"I need to get stronger," he said. "As I said the other day, I need to get my glutes strong again, my abs and my core back to where I used to have them. They are just not quite there yet. Obviously by playing you can't burn the candle at both ends. I need to get stronger physically and be back to where I was."
Woods, 38, suffered through his worst year as a pro, winning barely over $100,000 and failing to do better than a 25th-place tie at Doral. The 79-time PGA Tour winner started the year ranked No. 1 in the world and has dropped to 11th.