Green was optioned to Triple-A Scranton/Wilkes-Barre on Wednesday.
Green pitched a scoreless inning in relief in Tuesday's loss to the Reds, striking out two batters in his first appearance with the Yankees this season. The left-hander could be first in line for a promotion back to the big leagues if an opening in the rotation arises, but the Yankees have enjoyed sound health from all five of their starters to this point.