Minor, who went 6-12 with a 4.77 ERA for the Braves last season, missed most of the 2014 spring training with a groin injury but came back to start 25 games.
Braves general manager John Hart said that the team is trying to be proactive and not rush anything early in the spring.
''It kind of came from out of the blue,'' Hart said. ''Last year he started when he might not have been ready. Where it goes from here, I'm not real sure.''
Hart said Minor entered camp in shape and was throwing well before reporting the discomfort.