It's the first career DL stint for the eight-year veteran, who was scheduled to undergo an MRI on Wednesday afternoon to determine the severity of the injury. Right-hander Jesse Hahn was recalled from Triple-A Nashville to take his place on the roster, giving Melvin an additional long-relief option in the bullpen.
Melvin said Axford, who is eligible to return April 12, was expected to enter Tuesday's game in the eighth inning if the A's were trailing. It would have been his first appearance of the young season.
"When he threw a curveball, he felt a little tightness in his shoulder and threw another pitch and it just wasn't getting any better," Melvin said.
Hahn was in battle for a rotation spot during Spring Training, but he struggled in his final two outings -- finishing with an 8.80 ERA overall -- and was demoted March 26. He had four separate stints with the A's last year, posting a 6.04 ERA in nine starts, and is only two years removed from being their No. 3 starter.
Hahn will likely only be called on to pitch should the A's need multiple innings. They have three pitchers who can give them that, offering insurance behind Nos. 4 and 5 starters Andrew Triggs and Raul Alcantara. Those two are on tap to start Thursday and Friday, respectively.
Jane Lee is a reporter for MLB.com. Follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.