It's hard to say from Wikipedia whose *idea* it was, but it's old, almost as old as the Order of the Golden Fleece:
A predecessor order called the Brotherhood of the Mother of God Society was founded by King Christian I around 1460 and sanctioned by the Pope. Because this brotherhood was active in ecclesiastical areas, the king had the order confirmed by bulls from Popes Pius II (1462) and Sixtus IV (1474). At that time the image of the Virgin Mary holding the Christ Child hung on the chain of the order, while the chain showed elephants and towers.
Re: Danish kings and their favorites: Moltke's memoirs
A predecessor order called the Brotherhood of the Mother of God Society was founded by King Christian I around 1460 and sanctioned by the Pope. Because this brotherhood was active in ecclesiastical areas, the king had the order confirmed by bulls from Popes Pius II (1462) and Sixtus IV (1474). At that time the image of the Virgin Mary holding the Christ Child hung on the chain of the order, while the chain showed elephants and towers.