Green was originally scheduled to travel with the Yankees and pitch in Tuesday's game, but he instead threw a live batting practice session at the team's minor-league complex, Bryan Hoch of MLB.com reports.
Manager Aaron Boone indicated that the organization prefers to work some of its higher-leverage relievers into action cautiously, which explains the change in plans for Green. The 29-year-old is expected to fill a setup role in his sixth season with the Yankees.