Kipnis batted .524 (11-for-21) with two doubles, a home run and four RBIs in six games. His grounder to first on Friday gave the Tribe a walk-off win over Washington.
"It's a cool honor. It's definitely not something you try for or anything like that. It's something [where] you just put your head down and play the games -- you look up after Sunday and they'll let you know on Monday or something like that," Kipnis said. "That's all it is. ... It was a fun week. I got into a nice groove. I was seeing the ball real well. Probably the same thing goes for Kluber. He was in the same kind of good groove where he went out and was just locked down the whole week and had two great starts. It just means it was a good week. It's a cool award to have, though. Very happy to accept it."
Kluber's win on Sunday was his first at Progressive Field. Kipnis entered Monday riding a 10-game hitting streak, during which he's hitting .432 (16-for-37) with a homer and eight RBIs.
"I've been gaining confidence each time out, trying to build on the last one," Kluber said. "Just trying to pound the strike zone, really. Try to keep it simple, not make it too complicated."
The two players join Ryan Raburn and Justin Masterson as Indians players to be named AL Player of the Week in 2013.
"I think that's cool. I think that gives me the opportunity to brag about them, which I love to do," manager Terry Francona said. "Corey is just, right in front of our eyes, getting better. Kip got through that rough patch at the beginning of the year and has been such an impactful player for us, whether it's on the bases or at the plate. He just has that aggressive style that really helps us win games."
Mark Emery is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.