"I tried to play catch yesterday and it didn't feel good so we shut it down," Hudson said. "There's something in there that's inflamed. It's frustrating, but I'd rather be safe than sorry in April and be ready to go in September."
The good news for Hudson is that his MRI on Friday showed no structural damage and he hopes the 15 days will be enough time to recover.
Hudson last pitched Wednesday against the Pirates, but it was his previous start on April 13 that caused the problem in his shoulder.
"I didn't bounce back very well from my start in Colorado and I haven't felt good since," he said. "I was trying to push through it and battle because it didn't feel that bad once I got loose and warmed up. But every time I went out there, it was harder to get going."
With outfielder Chris Young on the DL with a shoulder contusion, the D-backs will now be further shorthanded. Outfielder Justin Upton, nursing a thumb injury, returned to the lineup against the Braves on Saturday night.
"I'm sure we're leading the pack in that category," manager Kirk Gibson said. "It's coming at us consistently, but we'll stave it off, there's no panic."
The club recalled relief pitcher Jonathan Albaladejo from Triple-A Reno to take Hudson's active roster spot.
Albaladejo was 1-1 with a 2.35 ERA and seven strikeouts in eight relief appearances with Reno this season.
"We we're coming down from Fresno and we got into Reno at 5 in the morning, that's when they told me," Albaladejo said. "I'm just going to try to go out there and keep doing what I've been doing, try to focus on throwing strikes and getting ahead in the count. Hopefully, I'll be calm and focused, but I don't know how I'm going to feel."
Hudson is 1-1 with a 6.00 ERA in three starts with the D-backs this season. He allowed two runs on six hits in 7 2/3 innings in his last start.
"It's scary, especially because I've never felt it before," Hudson said. "All the worst thoughts go through your mind. You hear so many stories about guys who don't bounce back from shoulder injuries. You just pray for the best."
Hudson's next start was scheduled for Monday against the Phillies and Gibson said Wade Miley could take his place unless he is used over the weekend. After Monday, the D-backs will reevaluate their pitching situation and go from there.