St. Louis general manager John Mozeliak did not clarify what incident led to the suspension, but said Miller had been suspended for a "violation of team policy."
According to St. Louis website stltoday.com, Miller has been involved in two alcohol-related incidents at a Springfield-area apartment complex, one as recently as last week, that may have led to the Cardinals' decision.
"I'm not going to get into specifics," Mozeliak told the website. "Let's just leave it at that."
Miller, 20, was the Cardinals' first-round pick in the 2009 Draft and signed a $2.875 million signing bonus with the team. He is 7-3 with a 2.97 ERA at Double-A Springfield after the Cardinals promoted him from Class A Advanced Palm Beach and stands as their top prospect in MLB.com's rankings
Miller did not accompany Springfield for its six-game roadtrip to San Antonio and Corpus Christi on Tuesday.
Cardinals farm director John Vuch said the suspension likely won't be too long. It was believed the organization was looking to scale back Miller's innings this season anyway -- he's thrown 122 frames after going 104 last year -- although Vuch clarified it was due to a personal issue with the right-hander.
"As always, we don't go into specifics about the nature of the violation, as discipline of this type is a personal issue between Shelby and the organization," Vuch wrote in an e-mail to The News-Leader. "I will say that the suspension was no less or more harsh due to his status as a prospect -- it simply falls in line with the policy we apply to all of our players."
"It's unlikely to be terribly lengthy," Vuch added.
Miller had lined up to pitch Thursday at San Antonio after recording just two outs and allowing four runs in his last start Aug. 10 against the Missions. He'd allowed three earned runs or fewer in all of his previous nine starts before taking the loss at home.
According to stltoday.com, Miller, Springfield manager Ron Warner and Vuch agreed to the decision over the phone in the past few days. The site said no other players had been involved in the apartment incidents.
The Houston, Texas native was an All-Star Futures Game selection in 2010 and '11 along with earning Florida State League All-Star honors earlier this season.