The 38-year-old, who has appeared in the showpiece event seven times previously, was expected to be one of the captain's picks at Gleaneagles.
However, after competing in just four competitions since returning from back surgery, Woods has ruled himself out altogether.
"My primary wish is for Tiger to be healthy and competitive, and I hope that he'll return to the game very soon," Watson is quoted as saying by BT Sport.
"Of course, I'm disappointed that Tiger Woods has asked not to be considered for the US 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 remain on identifying three players to join the U.S. team and give us the best chance for success at Gleneagles."
The 2014 Ryder Cup gets underway on September 26.