It is the first time in his career that the American has been overlooked for a session in the competition.
Woods lost both of his foursomes and fourballs contests during Friday's first day of play at the Medinah Country Club in Illinois.
Bubba Watson, Webb Simpson, Keegan Bradley and Phil Mickelson will take part in the opening two matches for the USA.
They will then be followed by Jason Dufner, Zach Johnson, Jim Furyk and Brandt Snedeker.
Saturday morning's foursomes:
Watson/Simpson vs. Rose/Poulter
Bradley/Mickelson vs. Westwood/Donald
Dufner/Johnson vs. Colsaerts/Garcia
Furyk/Snedeker vs. McIlroy/McDowell