This is the first research to investigate the adaptation of lactation milk production and physico-chemical milk properties of dairy goats adapted to warm climates and low altitudes to terrestrial climates and high mountain areas (altitudes of 1500–2000 m) in a grazing-based production system. Kilis goat is a local dairy goat breed of Türkiye, adapted to warm climates and low-altitudes (altitudes of 600–800 m). Animal material was obtained from the National Animal Genetic Resources Breeding Project carried out in Kilis province. Our aim was to compare the milk production and physico-chemical properties of milk from Kilis goats at high altitude with previously published data from the same year and age in low altitude breeding flocks to which they were transferred. Lactation milk yield and daily milk yield were influenced by birth type, offspring sex, and flock, while lactation length was influenced by kidding month (p < 0.05). Milk energy, fat/protein ratio, and macronutrients were significantly influenced by birth type (except protein), offspring sex, and flock (p < 0.05), whereas no differences were observed for kidding month (except lactose). Density and pH increased, and freezing point decreased with increasing altitude. The study concluded that Kilis goats reared at high altitude had a lower milk yield than those reared at low altitude, but there was no significant difference in the nutrient content of the milk. The association between milk production and the physico-chemical properties of milk suggests that goats may be sensitive to adaptation from low to high altitude, possibly reflecting the increased differential adaptive metabolic and physiological functions and energy demands of high milk production.