Barraclough was optioned to Triple-A St. Paul on Friday.
The 31-year-old righty hasn't looked good in his three major-league appearances this season, allowing four runs in 3.1 innings of work. He's been far better in the minors, striking out 38.7 percent of opposing batters en route to a 3.00 ERA, but the struggling Twins may prioritize giving opportunities to younger players down the stretch.