The veteran Slowey felt discomfort while warming up in the third inning on Saturday night during the Marlins' 7-4 loss to the Pirates.
Slowey is getting an MRI exam on Monday to determine the severity of the injury. He said he has been pitching through some soreness, but it reached the point where he couldn't go on Saturday.
"Our training staff has been great," Slowey said. "They said, 'When you feel like you can't compete, that's when you need to say something.'
"When I was warming up, I just realized, this is not something I can get through. I wasn't getting loose."
Ames was one of three pitching prospects the Marlins acquired from the Dodgers on July 6 for Ricky Nolasco. Like manager Mike Redmond, Ames attended Gonzaga. The right-hander was the 17th-round pick of the Dodgers in 2009, and he opened the season at Triple-A Albuquerque.
Since joining New Orleans, Ames made five relief appearances, and he didn't allow a run in seven innings, while striking out five with one walk.
Ames was with the Zephyrs on Saturday at Albuquerque when he was called into the dugout. New Orleans manager Ron Hassey played a joke on Ames, telling him he was being sent to Double-A.
As Ames turned to walk away, Hassey broke the good news. "You're going to the big leagues."
The reliever took a red-eye flight out of Albuquerque and arrived in Miami at about 10:30 a.m. ET.
"I was really excited," Ames said. "It was crazy."
Before being dealt to Miami, Ames made 30 relief appearances for Triple-A Albuquerque, and he was 2-2 with a 3.67 ERA. He logged eight saves.
During the 2010 offseason, Ames actually met Redmond a couple of times at the Gonzaga campus. Redmond, still playing in the big leagues, was hitting in the cages.
"[Redmond's] picture is up there in the locker room," Ames said. "We have his jersey up there from when he won the World Series with the Marlins."