Pluko was placed on the 7-day injured list at Triple-A St. Paul with a forearm strain, TwinsDaily.com reports.
The Twins signed Plutko to a minor-league contract Friday.
Plutko is seeking a return to the majors after spending the last two seasons in the Korea Baseball Organization, Jon Heyman of the New York Post reports.
Plutko signed with the LG Twins of Korea Baseball Organization on Thursday, Sung Min Kim of The Athletic reports.
Plutko recently accepted an assignment to Triple-A Norfolk after clearing waivers, Nathan Ruiz of The Baltimore Sun reports.
Plutko was designated for assignment Sunday, Rich Dubroff of BaltimoreBaseball.com reports.
Plutko has allowed a home run in his last five outings.
Plutko allowed two runs on two hits in one inning during Saturday's 5-3 win over Washington.
Plutko allowed three hits and a walk while striking out two over 2.2 scoreless innings in Saturday's 8-3 loss to the White Sox.
Plutko allowed a walk and no runs in two-thirds of an inning to earn the save in Monday's 9-7 win over Houston.