Right-hander Phillippe Aumont was called up from Triple-A Lehigh Valley to replace Stutes.
Adams said something has felt off with his arm for about two or three weeks, and noted there were "concerns" after getting an MRI. He plans on getting a second opinion while the Phillies are on a road trip on the West Coast in the next week.
"There's some stuff going on that we're concerned about," Adams said. "So we're going to go to San Diego, and I'm going to see [Dr. Neal ElAttrache] and see what he thinks and get his opinion on what he feels the next step's going to be and just go from there."
Adams last pitched on Wednesday, and though he said he felt fine during the game and directly afterward, he had trouble doing activities when he got home.
"I tried to lift my little boy up and I wasn't able to do that," Adams said. "Just lifting my arm up was pretty uncomfortable. I kind of made my decision then to get it looked at and take a step back and see what was really going on, and that's where we're at now."
Adams, who was also on the DL earlier this season with a strained back, signed a two-year, $12 million deal with the Phillies in the offseason. The 34-year-old is 1-4 with a 3.96 ERA in 25 innings.
With Adams out, and a day after the bullpen surrendered a six-run lead, it seemed like it could not get worse for Phillies relievers. Alas, it did, and Stutes hit the DL.
The 26-year-old said his arm had been a bit sore for a few days, and by Sunday, he and team doctors decided it would be best if he took some time off.
"[It's] something I've tried to pitch through," Stutes said. "We decided it's better to not let it become something more major."
Stutes had a 1.32 ERA in his first 11 appearances this season, but that number has ballooned to 5.17 after he allowed seven earned runs in his last three outings.
Aumont began the season with the Phillies, but he was sent down in May after compiling a 4.15 ERA, with 15 strikeouts and 10 walks in 13 innings.