Lehman, captain of an American team that matched its worst loss ever to Europe last week in the Ryder Cup, was eligible for the World Golf Championship because he is No. 38 in the world ranking.
I was looking forward to competing this week, but I felt an obligation to return home to honor one of the games all-time great players and gentlemen, Lehman said in a statement.
Nelson died Tuesday at his ranch in Texas. He was 94.
Lehman and Scott Verplank, who grew up in Dallas and has known Nelson since he was 17, had dinner with Nelson during the Byron Nelson Championship in May.