The award, determined by a select panel of MLB voters, recognizes the most outstanding relief pitcher during each month of the regular season.
Nathan was 11-for-11 in save opportunities in June, posting a 0.00 ERA in 12 appearances. He allowed just four hits in 11 2/3 innings, striking out 18 and walking just one. Nathan's 11 saves also tied Colorado's Huston Street for the Major League high in June.
"He's throwing the ball really, really well right now," Twins manager Ron Gardenhire said of Nathan. "The ball is coming out of his hand with a good angle. He's just got the variety of pitches -- from the curveball to the slider. He even throws a changeup every once in a while along with having the two-seamer. He's got them all, plus the hard fastball."
It's the third time that Nathan has received the Delivery Man of the Month Award. He previously won it in July 2006 and July 2008.
Nathan's scoreless streak goes back further than just June. The closer has not allowed a run over his past 20 outings, a scoreless streak of 28 2/3 innings dating back to May 21. During that stretch, Nathan has held opponents to a .113 batting average.
"Right now it just seems like a lot of my pitches are working," Nathan said. "It's not just the slider. My curveball has been decent. My sinker has been saving me again when I do need a pitch, because I'm behind in the count, and it's something other than what hitters have already seen. That pitch has been big for me."
Nathan, whose 1.35 ERA this season is the lowest among AL relievers with at least 30 innings pitched, also credits the consistent work he has been getting out of the 'pen for his recent string of strong outings.
"That keeps your feel where it needs to be, your arm slot where it needs to be," Nathan said. "You don't feel like your arm is floating around up there. You feel pretty much like you are locked in and just not thinking about things. Usually, when you are not thinking in sports, you'll do pretty well."
Since the start of the 2004 season only Francisco Rodriguez has recorded more saves than Nathan. Rodriguez has 227 saves over that span; Nathan has 221. Trailing closely behind those two are the Yankees' Mariano Rivera and the Brewers' Trevor Hoffman, both of whom have 220 saves during that time.
"The guy we have at the end, he's as good as they get," Gardenhire said.
Other relievers considered for the MLB Delivery Man of the Month for June were the Angels' Brian Fuentes (nine saves, 0.00 ERA), Seattle's David Aardsma (1-0, eight saves, 0.00 ERA), Street (1-0, 11 saves, 2.13 ERA) and Detroit's Bobby Seay (1-0, 0.00 ERA in 14 games).