The move was made retroactive to July 30.
Braun, a 14-year veteran, has appeared in four games this season, with three starts as a designated hitter.
He is hitting .231 with two RBIs this season. The former Rookie of the Year, MVP and six-time All-Star has a career average of .298 with 344 home runs and 1,130 RBIs.
The Brewers, who have not played since July 29 after four games were postponed last week against the St. Louis Cardinals because of a coronavirus outbreak on that team, did not announce a corresponding move.