It's called an "edicola"; from Latin "aedicula", "little temple", "little building". In English, a wayside shrine. Edicole (that's the plural) honoring the Virgin are usually called "madonnine" (singular: "madonnina"), or 'little Madonnas'. Traditional Catholic piety has set them up all over Europe, although especially in the very Catholic countries: Italy, Spain, and Poland. The madonnina you photographed above seems to date to the 20c, at least in its present version; it may go back much further, and have been repainted as it spalled or wore due to weather. There are several main kinds of edicole; this one is a niche-type, in which a painting has been recessed into a niche, to protect against the weather and also to create a shelf space for flowers. In some cases the niche is deep enough to accommodate the saying of Mass; that's most often seen in rural areas, where say once a year on some special feast, usually either a harvest feast or the feast of the saint honored, the priest goes out and does so, to bless the crops or community.
Edciole are most often considered public; but some are private. They are almost always cared for, though, by private individuals.
Bill Thayer
(The Web being what it is, I could not post a link to my site on madonnine, which shows a valley of types, and examples as far back as the 15c. Search Google for "edicole d'Italia", the site comes up first.)