The move was made retroactive to Tuesday, two days after he was reinstated from the 15-day IL following a stint with the same injury. He allowed one hit and threw 10 pitches in one-third of an inning in relief Sunday against the Cleveland Guardians.
In 12 appearances this season, the 36-year-old Thielbar is 1-0 with a 1.74 ERA, two walks and 10 strikeouts.
Also on Friday, the Twins recalled right-hander Josh Winder from Triple-A St. Paul.
Winder, 26, allowed two runs on three hits in two-thirds of an inning in his lone appearance for the Twins this season on April 30 against the Kanas City Royals.
He recently appeared in nine games for the Saints from May 7-June 3, posting a 2-1 record with two saves and a 6.60 ERA.
Twins LHP Caleb Thielbar goes back on IL with oblique strain