Fien, who was signed as a Minor League free agent before the season, has a 1.32 ERA in 25 appearances. The former Tigers reliever also has 26 strikeouts and eight walks in 27 1/3 innings without giving up a homer.
He threw two scoreless innings against the Indians on Sunday, and 22 of his 25 outings have been scoreless.
"He takes the ball just about any time you want him to," Twins manager Ron Gardenhire said. "He never really says he's sore or anything. He has a rubber arm and wants the ball. He has an above-average fastball and a great slider. He's not afraid to pitch inside so he's kind of one of those attackers."