Donaldson, who secured the winning point for Europe at last month's Ryder Cup, will face Reed - the only American in the 16-man field - Jonas Blixt and Paul Casey in the Mark McCormack group at the London Golf Club.
There are four groups of four and each has a round-robin style where everyone plays everyone else before the top two advance to the quarter-finals.
Volvo World Match Play groups in full
Arnold Palmer: Henrik Stenson, Thongchai Jaidee, Francesco Molinari, George Coetzee
Mark McCormack: Jamie Donaldson, Patrick Reed, Jonas Blixt, Paul Casey
Assar Gabrielsson: Victor Dubuisson, Stephen Gallacher, Shane Lowry, Pablo Larrazabal
Gustaf Larson: Graeme McDowell, Joost Luiten, Mikko Ilonen, Alexander Levy