Nadal withdrew from last month's Paris Masters with an abdominal muscle injury, meaning Novak Djokovic replaced him as world number one.
The Spaniard, 32, said that since he was still suffering with that injury, he would "take advantage of the moment" and have an operation on his ankle.
American John Isner takes Nadal's place at the eight-player event in London.
In a post on social media, 17-time Grand Slam champion Nadal wrote: "It has been a complicated year, very good at the tennis level when I was able to play, and at the same time very bad as far as injuries are concerned.
"Unfortunately, I had the abdominal problem in Paris last week and, in addition, I have a free body in the ankle joint that has to be removed in the operating room today.
"It is true that we had detected it for a long time and from time to time it bothered me. However, since the problem in the abdominal muscle also prevents me from playing in London, we take advantage of the moment to remove the free body and avoid future problems.
"This way I hope to be in full condition for the next season."
Nadal has retired from two of the three hard-court events he has competed at this season - the Australian Open and the US Open - but won the other, the Rogers Cup.
The Spaniard's absence from London means 14-time Grand Slam champion Djokovic will end the year as the world number one for the fifth time in his career: level with Roger Federer and Jimmy Connors, and one behind Pete Sampras.
Caption: Nadal during this year's French Open.
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