Here’s the 1972 origin of the term in the medical literature:
Jennett B, Plum F: Persistent vegetative state after brain damage. A syndrome in search of a name. Lancet. 1972, 1: 734-737. 10.1016/S0140-6736(72)90242-5.
Here’s a more recent article (2010) suggesting an alternative terminology and discussing the discomfort the medical profession feels using it, for both medical and human reasons.
The conception of a vegetative nervous system goes back to 1800 when Bichat divided the nervous system into animalic and vegetative . The former linked the person to her or his environment and was expressed by the muscles of voluntary locomotion and the organs of external senses. The latter identified the nutritional functions of the body. According to the Oxford English dictionary, 'to vegetate' is to 'live a merely physical life devoid of intellectual activity or social intercourse' and 'vegetative' describes 'an organic body capable of growth and development but devoid of sensation and thought'. To part, if not most, of the lay public and media, however, it has a rather pejorative undertone and seems (incorrectly) to refer to patients as being vegetable-like
Google Ngram shows a considerable increase in the use of the term “vegetative state” in the years after the 1972 article. A check of earlier uses, admittedly incomplete, picked up only use relating to plants, not human beings.