The research objective was to evaluate the effect of dietary incorporation of hemp seeds in goats fed with hay or mixed shrubs-grass rangeland on the production, FA profile and health-related lipid indices, antioxidant content and total antioxidant capacity of milk, with the purpose to increase the content of beneficial ingredients in milk and to improve its functional activity. Forty indigenous Carpathian goats were allocated into two groups according to the type of basic forage in their diet: hay (H) or mixed shrubs-grass rangeland (SG); each of them was further divided into two subgroups according to the presence of Hs in the concentrate mixture (250 g/kg) or not. Milk production was determined, and milk samples were collected and analyzed for fat, protein, lactose, and cholesterol content, as well as FA profile, lipophilic antioxidant content (α-tocopherol and retinol), and milk TAC. SG goats gave less milk (p < 0.01) but with higher milk fat (p < 0.001) and lower cholesterol content (p < 0.01) than H goats, while milk protein and lactose contents were not affected. Supplementing the diet with Hs caused a significant increase in milk production (p < 0.05) and milk fat content (p < 0.001) and a decrease in cholesterol content (p < 0.05). Grazing compared to indoor feeding but also supplementing the diet with Hs had the effect of decreasing the proportion of SFAs and increasing the concentrations of polyunsaturated FA (PUFA) in goat milk fat (p < 0.01). Fats in the milk of SG goats compared to H, but also in those supplemented with Hs, showed significantly higher proportions of vaccenic acid (VA), rumenic acid (CLA c-9,t-11) and omega-3 FA (α-linolenic acid (ALA), eicosapentaenoic acid (EPA), and docosapentaenoic acid (DPA)) which are considered healthy for consumers. The feeding system based on SG and the diet supplementation with Hs ensured the best nutritional and functional quality of milk, confirmed by the FA profile, antioxidant content, and by the value of health-related lipid indices (n-6/n-3 FA ratio and hypo-/hypercholesterolemia, atherogenic index (AI), thrombogenic index (TI), and health promotion index (HPI)). The results of our work will be useful for the development of optimal nutritional strategies that improve the FA profile and the antioxidants content in goat milk, with beneficial effects on human health.