The 31-year-old Moylan has appeared in 80 or more games in three of the last five seasons. He missed most of last season because of back surgery before needing another surgery for a torn rotator cuff and labrum.
Moylan is 19-9 with a 2.60 ERA in his career.
The Braves also declined to offer a contract to utility infielder and pinch hitter Brooks Conrad on Tuesday. He hit .223 with four homers and 13 RBIs last season.
The Braves have four arbitration-eligible players on their 40-man roster: right-hander Jair Jurrjens, left-hander Eric O'Flaherty, left fielder and infielder Martin Prado and center fielder Michael Bourn.