Miami also recalled outfielder Jake Marisnick from Triple-A New Orleans before Friday night's game at St. Louis.
Manager Mike Redmond said Dietrich hurt the wrist taking practice swings in the on-deck circle Tuesday against the Phillies, and then aggravated the injury the next day in the batting cage. He is batting .228 with five home runs and 17 RBIs in 49 games.
This is the second call-up of the season for Marisnick, who was batting .170 in 13 games with Miami.
Redmond said shortstop Adeiny Hechavarria, on the DL with a right triceps strain, was set to play Friday and Saturday for Class A Jupiter and rejoin the team Monday in Arizona.