Minor was awarded a raise from $3.85 million to his $5.6 million request, rather than the Braves' $5.1 million offer. Mark Burstein, Gil Vernon and Dan Brent announced their decision Friday, a day after hearing arguments.
The 27-year-old left-hander was 6-12 with a 4.77 ERA in 25 starts last year, when he missed the first month of the season because of shoulder soreness. He went 13-9 with a 3.21 ERA in 2013.
This year has seen the most hearings since teams went 8-6 in 2001. Baltimore outfielder Alejandro de Aza and Seattle right-hander Tom Wilhelmsen remained scheduled for hearings.