Green was outrighted to Triple-A Syracuse on Sunday, Chelsea Janes of the Washington Post reports.
The Nats designated Green for assignment earlier in the week but Green will remain in the Washington system, having passed through waivers unclaimed. A first-round pick in 2009, Green is merely an organizational depth piece. He has totaled 353 plate appearances in parts of five seasons at the major-league level (97 plate appearances since the start of the 2015 season).