Brown signed a minor-league contract with the Reds on Thursday.
Brown (shoulder) returned to action for Double-A Biloxi on Friday, retiring two of the five batters he faced en route to earning a hold in the team's 4-1 win over Montgomery.
Brewers manager Craig Counsell said Sunday that Brown has been shut down indefinitely due to right shoulder fatigue, Will Sammon of The Athletic reports.
The Brewers included Brown as part of their initial 60-man roster pool released Monday.
Manager Craig Counsell said Wednesday that Brown could pitch for the big club at some point this season, Adam McCalvy of MLB.com reports. "It's a name we don't talk about a lot, but a name who can help us this year," Counsell said in regards to Brown. "One of those we're maybe not counting on on Opening Day, but one of those guys who can impact us during the season."
Brown allowed two earned runs over six innings in a start with Triple-A San Antonio on Monday and owns a 3.99 ERA, 1.51 WHIP and 32:18 K:BB in 38.1 innings over seven Triple-A starts this season.
Brown will open the year with Triple-A San Antonio, Mike Rosenbaum of MLB.com reports.
Brown was invited to the Brewers' big-league camp Wednesday.
Brown (ankle) will make a start with Double-A Biloxi on Monday.
Brown (ankle) will begin a minor-league rehab assignment with the Arizona League Brewers on Thursday.