To take his spot on the roster, Chicago purchased the contract of Jake Petricka.
White Sox manager Robin Ventura said Troncoso complained of chest pains on Friday and was taken to a Twin Cities hospital, where he remained Saturday.
The 30-year-old, whom Ventura said knew about the condition after a flare-up three years ago while with the Los Angeles Dodgers, could still be released Saturday.
"There was no other thing to do but send him there," Ventura said. "It's serious stuff where you just don't take a chance. Let the medical people take care of it."
Petricka is 5-0 with a 1.31 ERA and 58 strikeouts in 54 2/3 innings between Double-A and Triple-A this season after a 5.39 ERA between Single-A and Double-A as a starter in 2012.
"It was a complete surprise because there was a lot of guys down in the pen, but there were a few guys in front of me, I felt. I'm just happy for the opportunity."
The 25-year-old is a graduate of Faribault High School about 50 miles south of Minneapolis. He makes his offseason home in the suburbs. He expects more than 30 friends and family members at Saturday's game in hopes of seeing his major league debut.