I can tell that it is called
blasone in Italian, no idea why the wikipedia article isn't properly linked.
As a literary device is as old as dirt. As a poetic genre, though, it has an interesting story.
Clement Marot didn't truly come up first with the idea, but revived and reinvented an already existing form of poetry that fell into disuse.
The original purpose of the blason in medieval poetry was to provide a most evoking, all-encompassing description of something, just as the description of a heraldic coat of arms to a heraldist conjures an unmistakable image of what it is supposed to represent, hence the name. It was recited with the cadence of an enchantment or a litany, at times monotonous, at times variegated. Pretty much an exercise in metric and wordsmithing. It had nothing to do with body parts or courting.
With time though, in the mind of contemporary writers, coat of arms and ladies became correlated since they deemed knightly feats and courtly love the twin ideals of the perfect courtier, as typified by Guillaume Coquillart's Blason des armes et des dames of 1484.
Yet the blason as we intend it came up some decades later. In 1535, Marot, in exile at Ferrara near the court of Renée of France (Duchess of the place), run a contest in which invited his poet friends to send to him a blason evoking a female body part. The winner would have received a pair of gloves from the Duchess. It was a huge success which ushered and popularized the genre.
For the record, the winner was Maurice Scève with the poem Le sourcil aka The eyebrow.
Another tidbit: as the blason became all the rage, the 'counterblason' became popular as well. Not the delicate Shakesperaean variety in which the exaggerated comparisons are rejected in favor of humble human beauty: the straight ridicule and shaming of perceived ugliness through natural metaphors (NSFW obviously).