Johnson said that while the cartilage in his knee was fully healed, he felt he would be better off spending the week practising rather than playing.
“After a lot of careful thought and consultation, I have decided that it is in my best interest if I withdraw from next week’s Hero World Challenge,” he wrote.
“I have informed captain Woods of my decision, which he fully supports and understands, and cannot wait to tee it up with him and my teammates next week in Australia.”
The US Presidents Cup team is missing world No.1 Brooks Koepka, who is rehabilitating an injured knee. His place was taken by Rickie Fowler.
The Americans, who have lost the event only once in 12 stagings, are favoured over Ernie Els’ International team that has also been hit by injury.
Australian former world No.1 Jason Day withdrew on Friday due to a back problem, replaced by South Korean An Byeong-hun.
South African Charl Schwartzel, a mainstay on the International team at the past four events, was unavailable for selection due to a wrist injury. He has not played since April.
The World Challenge is an exclusive 18-man tournament, which does not count as an official victory on the PGA Tour.