The 28-year-old Spaniard sustained the injury in practice last month and had been wearing a cast in training, forcing him to miss the Rogers Cup in Toronto and last week’s Cincinnati Open.
The year’s final Grand Slam event begins on Monday and Nadal said on Facebook yesterday: “I am very sorry to announce I won’t be able to play at this year’s US Open.
“I am sure you understand that it is a very tough moment for me since it is a tournament I love and where I have great memories from fans, the night matches, so many things.
“Not much more I can do right now other than accept the situation and, as always in my case, work hard in order to be able to compete at the highest level once I am back.”
The world No 2 and 14-times Grand Slam winner also took the title at Flushing Meadows in 2010. Despite missing the entire North American hardcourt campaign, Nadal had hoped to compete in New York, previously posting a picture of himself working on court with his uncle and coach Toni with a black wrist support clearly visible.
The left-hander won his ninth French Open in June but has not played since losing in the fourth round at Wimbledon to Australian Nick Kyrgios on 2 July.
Nadal has had to battle back from lengthy injury lay-offs several times in his brilliant career. After being sidelined for seven months with a knee problem, he returned in February 2013 to win ten titles including Grand Slams in Paris and New York.
Injuries also caused Nadal to miss the defence of his Wimbledon title in 2009 and his Olympic crown in 2012. The winner of 64 career singles titles, he has claimed four trophies this year.
He has set no time frame for a return to competition.
Meanwhile, Roger Federer has comfortably qualified for a record 13th consecutive ATP World Tour Finals, in contrast to 2013 when he squeezed in the week before the end-of-season tournament in London.
Federer, 33, claimed his sixth Western and Southern Open title in Cincinnati on Sunday with victory over Spain’s David Ferrer, the last key tune-up event for the US Open.
The result was good enough for him to become the third man to qualify for the eight-player event, behind world No 1 Novak Djokovic and Nadal.
Federer, who was won the Tour Finals six times, said: “It’s always one of the big goals I set myself at the beginning of the season. It’s always an absolute honour being part of the best eight. Getting a chance to win an extra trophy at the end of the season – which is so prestigious, one of the biggest ones we have in the game and one I’ve done so well at – is a great feeling.”