Manager AJ Hinch described the injury as a "scap spasm." Rodriguez was joined by Hinch and a team trainer on the mound to look at the "scapula," or shoulder blade, before the decision was made to remove him.
After throwing a strike to Chris Taylor, Rodriguez walked to the back of the mound, where he appeared to be in discomfort. He threw one warmup pitch to the screen and left the game.
"He had a spasm, and when we went out there, he was wanting to take a breath," Hinch said after his team's 8-3 loss. "He had a little bit of a hard time settling down. But he wanted to throw a pitch, and then we all saw that pitch, and then we took him out of the game.
"So, he'll be reevaluated [Tuesday], and we'll see how he comes out."
Rodriguez, facing the Dodgers six weeks after he used his no-trade rights to nix a deal to join them near the trade deadline, allowed five runs on five hits with one walk and one strikeout.
"His health is the No. 1 priority. When he tried to throw, he was very uncomfortable," Hinch said. "At that point, I'm just trying to get through the inning and reset."
J.D. Martinez, who homered twice off Rodriguez and drove in five runs, said he wasn't motivated by Rodriguez's decision not to come to Los Angeles. The slugger tried to text his former Boston Red Sox teammate when the deal was still in limbo but never got a response.
"You know, everybody makes their decisions, everyone's got their choices why they did it," Martinez said. "He texted me and apologized why he couldn't text back. It was a family decision. I get it, man. He's got to do what he's got to do for him. It's understandable. Obviously, we wanted him here, but it is what it is."
Trey Wingenter was summoned from the bullpen to replace Rodriguez and worked two innings for Detroit, striking out two on 29 pitches.
"It was definitely unexpected, those kinds of things," Wingenter said. "You hate to see your starter come out and feeling something may be wrong. But everyone was on high alert as soon as that happened."
Rodriguez took the loss, falling to 11-9 on the season.
The Associated Press contributed to this report.