"I spoke with Billy and he very badly wanted to play that last game on Wednesday," Reds manager Bryan Price said. "My understanding very close to the inception was that he would be going home and that it would most likely take several days before he would be back."
Under the rules, Hamilton will miss a minimum of three days and can miss up to seven games.
Peraza, 22, batted .295/.341/.393 with one home run and eight RBIs in 30 games for Louisville. Besides being able to play shortstop and second base, he can also play center field and has speed.
"I don't like the circumstances why I'm here, but I feel happy," Peraza said via translator Julio Morillo. "I've just come to do my job and help the team to win."
The Reds acquired Peraza, outfielder Scott Schebler and Minor League infielder Brandon Dixon from the Dodgers on Dec. 16 as part of a three-team trade that sent Todd Frazier to the White Sox.
Peraza had a nice showing in camp, but was one of the final cuts from the roster.
"I didn't get mad," Peraza said. "I went there to Spring Training to do my job. I don't control the decision that they make. After that, after they told me I was going to go to Louisville, I just focused and worked hard and played every day really hard in order to be on the team soon."
Peraza did not start on Friday, but Price noted he would have him start at least one game during the series in center field. A natural shortstop, he has played six games this season in center field and another four games there during spring.
"I've been playing more games in center field, so that's why I feel really comfortable right now," Peraza said.
• Pitcher Jon Moscot, currently on the 15-day disabled list with soreness in his surgically-repaired left non-throwing shoulder, is scheduled to have a rehab assignment start for Louisville on Sunday against Columbus. Moscot is scheduled to throw 75 pitches.
• Pitcher Anthony DeSclafani, who has been out all season with a left oblique strain, is slated to have a bullpen session on Saturday. It will be DeSclafani's first time on the mound since he suffered a setback last month during a rehab assignment.