Webb picked up two fifth-place votes and one ninth in results that were released on Monday. The Cardinals' Albert Pujols captured the award for the second time in his career as he finished just above the Phillies' Ryan Howard.
D-backs shortstop Stephen Drew also garnered a ninth-place vote.
Arizona has never had an MVP, but the organization does have five Cy Young Awards to its credit. Four of those were won by Randy Johnson from 1999-2002, and Webb added one of his own in 2006.
Webb finished second in the Cy Young balloting in 2007 and 2008. In 2008, he tied for the Major League lead in wins with 22, while compiling a 3.30 ERA.
The season could not have started better for Webb, who won his first nine starts to become the first pitcher to do so since Andy Hawkins won his first 10 starts in 1985. He won NL Pitcher of the Month for April by going 6-0 with a 1.98 ERA.
Drew established himself as one of the elite shortstops in the NL, as he hit .291 with 44 doubles, 11 triples, 21 homers and 67 RBIs.
Those numbers put him in some rarefied air. Only two previous shortstops -- Robin Young and Nomar Garciaparra -- have collected at least 40 doubles, 10 triples and 20 homers in a season.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.