Store uncut, unripe mangos at room temperature until they ripen, which can take a few days. Don't store green mangos in the fridge, or they will never ripen. Keep them at room temperature in a paper bag if you want to speed up the ripening process because the gas they release will help them ripen quicker. Once mangos are ripe, you can store them in your fridge for 4-5 days if you haven't cut them up yet.