The team could employ a four-man rotation for the foreseeable future.
Miller, 23, has recorded a 4.29 ERA with 73 strikeouts and 54 walks over 109 innings. He made five relief appearances as a rookie in 2012.
"How long that lasts, I'm not going to say [it will be through the end of] the month," Manager Mike Matheny said. "We'll see how guys look and feel. [Miller is] ready to go [in the bullpen]. As far as how we use him, it's how we need him."
Wainwright, 32, has posted a 1.83 ERA with 115 strikeouts and 27 walks over 138 innings this season.
The 6-foot-7 right-hander will make his first start of the second half on Tuesday, against Tampa Bay, affording him 10 days rest since his last start.
The Cardinals opened Saturday one game back of Milwaukee in the National League Central.
- Chris Johnson