PHOENIX — A.J. Puk, the prized prospect projected to be in the A’s rotation at some point this season, has been shut down with biceps soreness, according to a source.

Puk had an MRI exam and there is no indication the left-hander has any major structural damage, the source told The Chronicle, adding that the injury is not believed to be serious and that Puk should resume throwing “sometime fairly soon.”

Even so, there is automatic concern when a player of Puk’s prominence is shut down for any reason, particularly with no time frame for his return.

Puk was sent to minor-league camp Sunday despite having only one poor inning all spring, his final inning Thursday against Seattle. He allowed four runs, the only earned runs in his 102/3 innings of work.

Scouts said that Puk was throwing his two-seamer about 93-94 mph, which is in his normal range; he did not throw his four-seamer, which typically registers 97-98 mph, very much throughout the spring. He has not thrown since that outing.

A’s starter Jharel Cotton was shut down with a torn ulnar-collateral ligament last week and had Tommy John surgery Wednesday. Oakland signed right-hander Trevor Cahill on Monday and Tuesday added ex-A’s starter Brett Anderson on a minor-league deal.

Now Playing:

Innovative ticket program: How much would you like to pay to see the A’s this year? You can decide for yourself beginning April 4. The A’s are allowing fans to pay their own price for tickets — a $1 minimum donation is required — in section 322 every Wednesday this season, with all proceeds going to fund charitable efforts and initiatives through the Oakland A’s Community Fund.

“This program is unprecedented and we’re excited to be — what we believe — the first team to create a ticket section to completely benefit charity,” vice president of communications Catherine Aker said.

Fans interested in tickets for Community Impact Wednesdays can visit athletics.com/impact. Section 322 is located in the third deck, slightly up the third-base line from home plate.

Union update: The A’s had their spring meeting with the Players Association, and afterward, union head Tony Clark told The Chronicle there are still concerns over the slow free-agent market.

“We haven’t seen in a long time what we’re seeing this offseason,” he said. “One of the things that is resonating in each locker room is the idea that if teams are not just evaluating players differently but are less inclined to be the last team standing, how is that affecting everything that goes on during the offseason, whether free-agent related or trade-related? ... Guys are questioning the competitive integrity of the system.”

The union’s issues with the A’s minimal spending (the payroll stands at $70.5 million) were evident when the team was included in a grievance over failure to spend revenue-sharing checks.

Briefly: The team announced that Cotton came through surgery well in Arlington, Texas, and he will rejoin the team Sunday in Oakland to begin rehab. ... Cahill will throw up to 40 pitches Thursday in his first game with the A’s; Andrew Triggs will start.

Susan Slusser is a San Francisco Chronicle staff writer.

Brewers 4, A’s 3

Notable: Daniel Mengden all but assured himself a rotation slot by allowing five hits, one walk and two runs in 61/3 innings; he struck out three and threw 85 pitches in his final start of Cactus League play. ... Mengden’s lone slip-up was a two-run homer by Eric Thames in the sixth. ... Franklin Barreto had two hits and is batting .305 for the spring, while another minor-league infielder, Sheldon Neuse, was 2-for-4 and is batting .320. ... Chad Pinder hit his third homer of the spring, a solo shot in the sixth. ... The A’s entered the game with 16 errors, second fewest in the majors, but made two (Mengden and Pinder).

Quotable: “It was the same thing I struck him out on, a 3-2 backdoor slider, trying to go to the same thing 1-0 for a double play. It leaked back over the middle and he did what he’s supposed to.”

— Mengden on the pitch Thames hit for a two-run homer.

Thursday: at Brewers, 1:05 p.m.

— Susan Slusser