The move was made before Wednesday's game against Kansas City, the first trip to the disabled list in Reed's seven-year major league career.
In 41 games in his first season with the Twins, Reed is 1-5 with a 4.83 ERA. He has allowed eight home runs in 41 innings. Five of those have come in his past 16 appearances, over which he has a 9.42 ERA with 24 hits allowed in 14⅓ innings. Reed signed a two-year, $16.75 million contract with the Twins before the season.
Right-handed reliever Alan Busenitz was recalled from Triple-A Rochester for the third time this year.