Before the announcement was made Friday, A's manager Bob Melvin said, "We want to make sure [Hill] is as close to 100 percent as he can be, and we're not certain after throwing a flat ground [session]."
Hill, the American League Pitcher of the Month for May, last pitched Saturday, departing in the seventh inning with a mild groin strain.
"There's still some issues going on with the groin, but we're going to figure it out and see how we progress from there," Hill said Friday. "It's my drive leg, pushing off the mound, that's the biggest thing. Just a little bit of residual effects left in there, so we're working every day to get it better."
Hill compiled a 5-1 record and 2.13 ERA and struck out 37 in 38 innings to earn his first career Pitcher of the Month Award.
"I think it's great," Melvin said. "Well deserved. Borderline dominant starts, whether it's strikeouts or lack of hits, runs, all of the above."
"You just continue to work, and that's it, and you try to be the best that you can every single day you go out there and take advantage of the time that we have," Hill said. "It's really not so much about the results, it's about the process. That's where you find the real joy in competing and being ready for every fifth day."
• After optioning starter Eric Surkamp to Triple-A Nashville on Thursday, the A's recalled right-hander J.B. Wendelken to take his roster spot Friday. Wendelken joins the A's for the second time this season, after making his big league debut last month. He has a 4.58 ERA in 19 relief appearances for the Sounds.
Jane Lee has covered the A's for MLB.com since 2010. This story was not subject to the approval of Major League Baseball or its clubs.