Minor has not pitched for the Braves this season.
Minor will miss the rest of the 2015 season with hopes of returning for spring training next year. He will be a non-tender free agent candidate in the off-season after winning $5.6 million in his arbitration case in February.
Atlanta placed Minor on the 60-day disabled list earlier this month. On May 2, Braves President of Baseball Operations John Hart told reporters that the team didn't see the left-hander "coming back anytime soon."
Minor missed parts of 2014 with shoulder injuries and was limited to 145 1/3 innings pitched. His shoulder discomfort continued into spring training this year, and he had yet to appear in a game.
In five seasons with Atlanta, Minor, 27, has gone 38-36 with a career 4.10 ERA.
- Erick Fernandez