late 14c., allopicia, "falling of the hair," also a form of leprosy involving loss of facial hair, from Medieval Latin alopecia, from Greek alōpekia, a disease of the skin, also alōpekiasis, from alōpēx, alōpekos "fox." Also known as fox-sickness. Usually explained as transferred to the human condition from the animal's susceptibility to mange.
The term alopekia is derived from [alōpēx], a fox, and would seem to be intended to represent a kind of baldness with scattered hairs, which we meet with in animals suffering under the mange—for example, the canine genus, of which the fox is an example. [Medical Times and Gazette, Oct. 22, 1870]
Other theories are that it is so named "from the fox's being supposed to lose its hair sooner than any other quadruped" [Hoblyn's "Dictionary of Terms Used in Medicine"].
Burne the heade of a great Ratte and myngle it wyth the droppynge of a Beare or of a hogge & anointe the head, it heleth the desease called Allopicia. [Humphrey Llwyd, "The Treasury of Healthe," 1585]