It depends on the type of ribbon. In general, satin ribbon can be ironed, and as far as I can see from this image, yours is satin ribbon. When it comes to ironing other types of ribbon which are more delicate, such as chiffon ribbon, you probably should not heat these. For chiffon and other delicate types of ribbon, try soaking them in water and then straightening them to dry. This could help with reducing the wrinkles on the ribbon.