Wieland joins three other Padres starting pitchers on the DL. Tim Stauffer, Cory Luebke and Dustin Moseley are also currently out with injuries.
Wieland said he experienced discomfort while throwing curveballs in his start on Sunday, and he told the training staff. An MRI on Wednesday showed no structural damage.
"We're going to take a step back with Joe," Black said. "He's had some tests. Everything is structurally fine, so we're going to let him rest for the time being."
The Padres will make a corresponding move to add a position player for the upcoming series against the Phillies that starts Friday in Philadelphia. Wieland's scheduled start was Saturday. Instead, Edinson Volquez will make Saturday's start on regular rest, as the Padres have Thursday off. Volquez, who last pitched on Monday, was scheduled to start Sunday. Clayton Richard is scheduled to start Friday, and Jeff Suppan is expected to start Sunday.
Stauffer, who landed on the DL with a strained right elbow, could join the starting rotation soon. He is expected to make a final rehab start with Class A Lake Elsinore on Wednesday night. Stauffer could rejoin the Padres and start either Monday or Tuesday against the Nationals, with Anthony Bass starting the other day, Black said.
Wieland said he has never had a previous elbow issue. He experienced discomfort in his last start, when he allowed two runs in 5 2/3 innings against the Marlins.
"Just on curveballs last start, I felt a little discomfort," Wieland said. "I told the training staff after."
Wieland is 0-4 with a 4.55 ERA this season during his first stint in the Major Leagues.
"Hopefully, it's just a week or two of rest or whatever and we're back," Wieland said. "I haven't had any actual pain, just discomfort."
As for the Padres' other injured pitchers, Moseley is out for the season following shoulder surgery, and Luebke is expected to receive a second opinion this week after he said an MRI showed possible damage to the ulnar collateral ligament in his left elbow.
Stauffer and left fielder Carlos Quentin were scheduled to play in a game with Lake Elsinore on Wednesday night.
"Those guys are getting closer, so that's a good thing," Black said.
Sarah Trotto is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.