The injury to Duensing occurred in the 9th inning of Thursday's 8-5 victory over the Royals. Duensing was replaced by Glen Perkins after giving up two runs in the inning.
According to 1500 ESPN, Thielbar will be available for Friday night's game against Cleveland.
He's been serviceable over the past two seasons. In 93 2/3 innings in the Majors, Thielbar has struck out 74 batters and walked 30. He has a 2.59 career ERA. His best stretch was 2013 when Thielbar posted a 1.76 ERA in 46 innings.
The Twins chose to go with Thielbar, who like Duensing is a lefty, instead of right-hander Lester Oliveros.
In two appearances this season, Oliveros has struck out five in three innings, while allowing just two hits and walking one.
He was pretty tough against lefties last year, in 17 1/3 innings, Oliveros allowed three runs on 10 hits with seven walks, while striking out 25.
But, while Thielbar is on the Twins 40-man roster, Oliveros is not – adding him would require the Twins to place someone on waivers.
In seven games with the Twins last season, Oliveros faced eight left-handed hitters and they were hitless against him.