Cespedes was slated to make his second straight start at designated hitter against the Rangers, before the A's opted to rest him and make Nate Freiman their DH.
Cespedes initially injured the shoulder on the club's last homestand, though it hasn't necessarily affected his swing. He went 6-for-19 with nine RBIs on the A's six-game road trip and is batting .373 with three home runs and 13 RBIs in his last 13 games in September, eight of which have resulted in multihit performances.
Losing him for any period of time, then, would be significant.
"I cross my fingers and hope not," Melvin said. "Hopefully we can use him in a DH role. Pretty important guy to have."