"The soreness has to decrease, and there's a strengthening component to this. We've got to make sure he can swing the bat and have confidence that he can field his position," Padres manager Bud Black said.
The Padres recalled right-handed pitcher Thad Weber to give the team depth. Weber appeared in one game with the Padres on April 13, allowing two earned runs in 3 2/3 innings of relief. Weber was 2-0 with a 0.82 ERA in two starts in Triple-A.
Ross was disappointed with the news but understood the team wants him to get healthy again before he returns to the rotation.
"It's definitely frustrating," Ross said. "It's my off-shoulder, and I can still pitch just fine. But they've got my best interest at heart."
Ross suffered the injury to his non-throwing shoulder on the follow-through of his swing during the third inning against Dodgers pitcher Clayton Kershaw after getting his first Major League hit. Ross winced in pain as he ran up the line. But he remained in the game, pitching 4 2/3 innings in a no-decision.
Ross said the shoulder continues to feel better each day.
"I'm definitely feeling better today than I was yesterday," he said. "This will give me time to strengthen the shoulder. I'm pretty optimistic about it."
The Padres went through a similar ordeal two seasons ago when pitcher Dustin Moseley twice suffered subluxation to the shoulder of his non-throwing arm. Moseley had surgery following the 2011 season to repair a dislocated shoulder, torn labrum and stretched capsule.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.