It's the first time Hernandez has won the award, and he's the first Mariner to be selected since former right-handed closer J.J. Putz in June 2007.
Others receiving consideration for the award were Twins closer Joe Nathan, who allowed no earned runs in 11 2/3 innings and had 11 saves; Red Sox right-hander Josh Beckett, who was 4-1 with a 1.51 ERA; and Rangers right-hander Kevin Millwood, who went 4-1 with a 1.30 ERA.
Hernandez will receive a specially designed trophy and a Sharp Aquos television to commemorate the award.
Hernandez, who started Friday night's series opener against the Red Sox at Fenway Park, allowed fewer runs than any Major League pitcher who logged at least 20 innings during June, and his overall performance was highlighted by a 5-0 shutout victory over the Padres in an Interleague game in San Diego on June 16.
The righty ended the month with a stellar eight-inning effort against the Dodgers on Saturday, allowing one unearned run.
"The thing Felix has done is applied himself to the team concept and opened up," Adair said. "It has been a pleasure just being around him. With guys like Felix, a pitching coach just gives him the ball, sits back and watches."
But the first month and a half of the regular season were only so-so, the low point coming on May 19, when he surrendered a season-high 11 hits and five stolen bases to the Angels in a 6-5 loss at Safeco Field.
Manager Don Wakamatsu was critical of the effort, expressing his thoughts to the media and later to Hernandez.
He has been a different pitcher since that start, reeling off one outstanding effort after another.
"I have seen such a change, not only on the field, but in the way he walks around and carries himself," Wakamatsu said on Friday. "We all know when he turned things around, and it wasn't because of me. A lot of things clicked when he started to become more efficient, and controlling the running game made his stuff better.
"He became a little more efficient, but the competitive nature has always been there. It was like trying to taming a wild horse."
Entering Friday night's game against the Red Sox, Hernandez had an 8-3 record, 2.54 ERA and ranked fourth in the AL with 107 strikeouts.