The move was necessary to fit right-hander Austin Adams, who was recalled from Triple-A Rochester on Thursday, on the team's 40-man roster. Right-hander Trevor Hildenberger was sent to the minors in a corresponding move.
Reed, 30, hasn't pitched in the majors this season but has been rehabbing a sprained thumb on his left hand in the minors. He had struggled, posting a 14.40 ERA in five appearances.
He signed a two-year, $16.75 million contract with the Twins as a free agent in the 2018 offseason. He went 1-6 with a 4.50 ERA in 55 appearances with a career-worst strikeouts-per-nine-innings rate of 7.1 last season for the Twins.
He is 19-27 with 125 saves and a 3.53 ERA in eight seasons.