The winners were announced on MLB Network on Sunday.
Cano, 30, also earned a more traditional honor this offseason: the Rawlings Gold Glove Award for American League second basemen, Cano's second such honor.
Cano led all AL second basemen with 726 chances this year, finishing second in the league with a .992 fielding percentage while making six errors.
"There are a lot of ways you can contribute to a team win," Cano said. "It's not always about offense. Sometimes saving runs is as important as scoring runs."
Cano could also figure to be in the mix for the Defensive Player of the Year in the 2012 Greatness in Baseball Yearly Awards (GIBBYs), which are based on voting by media, front-office personnel, MLB alumni and the Society for American Baseball Research, as well as fan balloting on MLB.com.
Starting on Monday through Dec. 2, fans will be able to cast their ballots at MLB.com for the year's top defensive star.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.