The award is selected by CBSSports.com's Jeff Borzello, in partnership with the U.S. Basketball Writers Association.
Woodard's 12 assists in Tuesday's game were the most for an OU player since Terrell Everett had 15 against Baylor in 2006.
The Sooners will travel to Houston to play former conference rival Texas A&M on Saturday at the Toyota Center as part of a doubleheader.
Oklahoma will take on the Aggies at 6 p.m., after the Houston-Rice game at 3:30 p.m.
The game will be televised by ESPNU and is part of the inaugural Big 12/SEC Challenge.
Going into the final game of the series, the Big 12 holds a 6-3 advantage.
The Big 12 has won three consecutive series with other conferences, having beaten the Pac-10 in 2009 and 2010.