Donald, 38, shot a closing 67 for a 16-under total, five shots adrift of Kim.
Kim, 21, shot a second-round 60 to take command in North Carolina, and sealed his first PGA win with a 67 on Sunday.
Spain's Rafa Cabrera-Bello shared fifth and is in Clarke's side, with three wild cards to be added next week.
Clarke's fellow Northern Irishman Graeme McDowell, who holed the winning putt in 2010 and has played in the last four European sides, was one of the players to tie for fifth with the Cabrera-Bello.
Donald's compatriots Matt Fitzpatrick and Andy Sulllivan secured their automatic places in Europe's Ryder Cup team following the European Tour's Czech Masters, which also finished on Sunday.
They join Rory McIlroy, Danny Willett, Henrik Stenson, Chris Wood, Sergio Garcia, Justin Rose and Cabrera-Bello in Clarke's team for the matches at Hazeltine in Minnesota next month, as Europe seek a fourth consecutive win over the US.
Kim is the fifth South Korean to win on the PGA Tour and the youngest to triumph in the Wyndham Championship since Ryder Cup icon Seve Ballesteros claimed the title in 1978.
England's Luke Donald sent a timely reminder of his form to Ryder Cup captain Darren Clarke as he finished second in the Wyndham Championship behind South Korean Si Woo Kim.