The move comes one day after the 40-year-old Arroyo told reporters that there is a possibility his 14-year major league career might be over as he deals with a strained right shoulder.
"We tried to patch it up and it worked for a while, but I've been hit around the yard for a while now," Arroyo said after allowing five runs and seven hits in three innings against the Los Angeles Dodgers.
"It gets stiff. The cortisone isn't working anymore. Have I thought, 'This time might be my last time on the field?' Yeah."
Arroyo, who owns a 3-6 mark with a 7.35 ERA, is attempting a comeback after missing 2 1/2 seasons with arm and shoulder issues, including Tommy John surgery.
"It's a combination of things," Reds manager Bryan Price said. "His velocity is down again. ... I'll talk with Bronson and see how he's doing. It's not just a challenge with his stuff. It's a physical challenge."
Cozart, who is nursing a strained right quadrieps, is batting .320 with nine homers and 33 RBIs in 58 games this season.
The Reds called up outfielder Jesse Winker from Triple-A Louisville and right-hander Ariel Hernandez from Double-A Pensacola.
Winker, who will make his second stint with the Reds, is batting .317 with two homers in 263 plate appearances with the Bats.
Hernandez, who has a 2.18 ERA in 33 innings with the Blue Wahoos, struck out five without surrendering a hit in 2 2/3 scoreless frames against the Milwaukee Brewers on April 24.