The team's ace was set to have a cortisone shot on Wednesday and will not make his next scheduled start on Saturday against the Houston Astros. The A's did not give a timeline on whether Montas will be able to pitch again before the All-Star break.
Montas figures to be one of the most coveted pitchers available at the Aug. 2 trade deadline if he is healthy. He is one of the lone holdovers from the team's preseason purge in which the team traded key pieces such as first baseman Matt Olson, third baseman Matt Chapman and starting pitchers Chris Bassitt and Sean Manaea.
"We're still in the process of determining which direction we want to go," manager Mark Kotsay told reporters and referred questions to the team's head athletic trainer, Nick Paparesta.
"Everything looked great with the rotator cuff and the labrum," Paparesta told reporters. "Just some inflammation within his shoulder. ... We'll go day-to-day and cross that bridge when we get there."
Montas was removed from his last start, on Sunday against the Seattle Mariners, after just one inning. He allowed a home run to Mariners rookie outfielder Julio Rodriguez on his first pitch and threw 13 overall as his fastball averaged 93.8 mph, down from 96.2 mph entering that start.
Montas, 29, took the loss on Sunday to fall to 3-9 overall with a 3.26 ERA in 17 starts. He finished sixth in the Cy Young voting last season when he was 13-9 with a 3.37 ERA and 207 strikeouts in 32 starts.