Twins chief baseball officer Derek Falvey confirmed Simmons tested positive for COVID-19 and has experienced very mild symptoms, according to MLB.com's Betsy Helfand.
The Twins have a number of people going through the contact-tracing process, Helfand adds.
Simmons played all nine innings during a 4-2 loss to the Boston Red Sox at Target Field on Tuesday.
Last month, the 31-year-old said he wasn't interested in taking or advocating for the COVID-19 vaccine.
The Twins selected the contract of utility player JT Riddle from the club's alternate training site to replace Simmons on the roster.