Cotton won't officially be recalled until then, and the A's will have to make another move in Cleveland next week, with right-hander Daniel Mengden the likely fill-in option to start against the Indians.
Graveman was sidelined by the same shoulder injury from April 15-26, and it's assumed he'll be out even longer this time.
"Any time this happens a second time," A's manager Bob Melvin said, "you want to be a little bit more careful with it.