Minter was charged with a blown save in Sunday's 4-3 loss to the Mets after allowing two runs on two hits while managing to get just one out.
Minter (5-1) picked up the win in Sunday's victory over the Guardians, giving up one hit in a scoreless 10th inning.
Minter (2-1) struck out the side in a perfect eighth inning Sunday to record the win over the Marlins.
Minter (finger) retired two of the five batters he faced Wednesday in Atlanta's 10-9 Grapefruit League win over the Blue Jays, striking out one while giving up an unearned run on one hit and one walk.
Minter (finger) is expected to make a Grapefruit League appearance soon, Mark Bowman of MLB.com reports.
Atlanta and Minter avoided arbitration by agreeing to a one-year, $6.22 million contract, Kiley McDaniel of ESPN.com reports.
Atlanta reinstated Minter (shoulder) from the 15-day injured list Monday.
Minter (shoulder) will make a rehab appearance at Triple-A Gwinnett on Tuesday, David O'Brien of The Athletic reports.
Minter (shoulder) threw a bullpen session Saturday, Justin Toscano of The Atlanta Journal-Constitution reports.
Atlanta placed Minter on the 15-day injured list Saturday with left shoulder inflammation, Justin Toscano of The Atlanta Journal-Constitution reports.