The Angels also sent struggling slugger C.J. Cron back to the minors Tuesday.
Green is batting .329 with four homers and nine RBIs in 32 games in Salt Lake. The 27-year-old veteran spent a week on the Angels' roster in April.
Cron is batting just .204 this season with the Angels, failing to capitalize on an opportunity to become the Angels' everyday designated hitter after Josh Hamilton's departure for Texas.
Cron has played mostly against left-handed starters lately, and had started just three of Los Angeles' last 13 games.