Minter (hip) had his rehab assignment transferred to Triple-A Gwinnett on Monday, David O'Brien of The Athletic reports.
Minter made an appearance with High-A Rome on Saturday, allowing an unearned run and a hit while striking out three batters over an inning on the mound. The left-hander will now take the last step in his recovery from the left hip inflammation that has kept him out since May 30, joining the Triple-A roster. Minter will likely make multiple appearances with Gwinnett before being activated from the 15-day injured list in the near future.