I know that Varro in his De Agri Cultura mentions physicians for animals. He says (I'll give the Latin and then the English):

"Quarta pars est de sanitate, res multiplex ac necessaria, quod morbosum pecus est vitiosum, et quoniam non valet, saepe magna adficiuntur calamitate. Cuius scientiae genera duo, ut in homine, unum ad quae adhibendi medici, alterum quae ipse etiam pastor diligens mederi possit. Eius partes sunt tres. Nam animadvertendum, quae cuiusque morbi sit causa, quaeque signa earum causarum sint, et quae quemque morbum ratio curandi sequi debeat. Fere morborum causae erunt, quod laborant propter aestus aut propter frigora, nec non etiam propter nimium laborem aut contra nullam exercitationem, aut si, cum exercueris, statim sine intervallo cibum aut potionem dederis. Signa autem sunt, ut eorum qui e labore febrem habent adapertum os umido spiritu crebro et corpore calido. Curatio autem, cum hic est morbus, haec: perfunditur aqua et perunguitur oleo et vino tepefacto, et item cibo sustinetur, et inicitur aliquid, ne frigus laedat; sitienti aqua tepida datur. Si hoc genus rebus non proficitur, demittitur sanguis, maxime e capite. Item ad alios morbos aliae causae et alia signa, in omni pecore quae scripta habere oportet magistrum pecoris."

The fourth division is that of health — a complicated but extremely important matter, inasmuch as a sickly herd is a losing investment, and men frequently come to grief because it is not strong. There are two divisions of such knowledge, as there are in the treatment of human beings: in the one case the physician should be called in, while in the other even an attentive herdsman is competent to give the treatment. The topic has three heads: we must observe the cause of the several diseases, the symptoms displayed by such causes, and the proper method of treatment to be followed for each disease. In general, sickness is caused by the fact that the animals are suffering from heat or from cold, or else from excessive work, or, on the other hand, from lack of exercise; or in case food or drink has been given them immediately after working, without a period of rest. The symptoms are that those which have fever from overwork keep the mouth open, pant fast with moist breath, and have hot bodies. The following is the treatment in such cases: The animal is drenched with water, rubbed down with oil and warm wine, and, further, is sustained with food, and a covering is thrown over it to prevent a chill; in case of thirst tepid water is administered. If improvement is not obtained by such treatment, blood is let, usually from the head. Other diseases have other causes and other symptoms, and the man in charge of the herd should keep them all in written form" (Varro, De Agri Cultura, 2.21-23).

There's another older text from Egypt called the Kahun Papyrus, dated ca. 1900 BC which dealt with the medical treatment of women and animals (source: "The Old Egyptian Medical Papyri by Chauncey D. Leake, University of Kansas Press, 1952). I'm not sure that's the oldest reference to what we would think of as the "veterinary profession," but it's pretty darn old. Animal physicians are also mentioned in Mesopotamian sources (Code of Hammurabi, reign: 1792-1750).

The Greeks had names for horse doctors (hippiatroi), and the Romans had various names for physicians who dealt with animals, such as: equarius medicus (horse doctor), mulomedicus (mule doctor), medicus veterinarius, medicus iumentarius (beast-of-burden doctor), and even medicus pecuarius (sheep/cattle doctor). All of these physicians would have dealt with large animals, animals of industry, such as horses and oxen and sheep and cattle, which is what the roots of veterinary science would have been: the caring of stock.

If you'd like to see other Latin sources on veterinary sciences, I would recommend: M. Porcius Cato's De Agricultura, Vergil's Georgics (Book 3 deals with animals, while Book 4 deals with apiculture), and Palladius' De Veterinaria Medicinia (Book 14). For Greek I would recommend the CHG (Corpus Hippiatricorum Graecorum), which deals with horsemanship and the caring of horses.