Nine to 10 Days From Packaging Date. According to Mountain View Mushrooms, fresh mushrooms can be stored at 34 to 40 degrees F for up to 10 days from the date of packaging.If purchasing store-bought mushrooms, the packaging date will be printed on the storage container or plastic wrap.Artem Kononenko/Demand Media.ine to 10 Days From Packaging Date. According to Mountain View Mushrooms, fresh mushrooms can be stored at 34 to 40 degrees F for up to 10 days from the date of packaging.