Pinder was initially thought to just be feeling whiplash after colliding with the wall in right-center on Friday night, but Melvin said he started to feel worse Saturday.
"He hasn't felt too terribly great here. It started yesterday afternoon. We actually sent him home for the game yesterday," Melvin said. "He's a tough guy and he wants to play, but we're just not at the point right now where he can. Now that he is in the [concussion] protocol, he has to pass the proper test to get back. [It] could be a little while."
Pinder, batting .238 with 15 homers and 42 RBIs in 87 games this season, was back with the team on Sunday. After playing in the outfield for the first time this season in his professional career and impressing, Melvin hopes Pinder can get back on the field before the end of the season.
"He certainly wants to get back, because he's had a strong year for us, and wants to finish up strong," Melvin said. "But I really couldn't handicap at this point, and I certainly couldn't rule out the fact that he doesn't come back."
In addition, Powell hasn't played since Sept. 16 because of swelling on his left knee. Melvin said that Powell is "potentially on the same timetable" as Pinder.
With the two outfielders unavailable, the A's welcomed the return of Jake Smolinski to the lineup. He was in the starting lineup on Sunday. Smolinski had shoulder surgery in March and worked his way back to the team at the start of September, but was still working his way back to full strength on throws.
"It's been on schedule," Melvin said of Smolinski. "He's been available since the Detroit series. The timing is actually pretty good, now that he can play, with both [Pinder] and Powell out."
Alex Simon is a reporter for MLB.com based in the Bay Area. Follow him on Twitter at @alexsimon99. This story was not subject to the approval of Major League Baseball or its clubs.