The research studied the effects of dietary supplementation with Camelina sativa fresh forage on the chemical and fatty acid composition of milk and Caciotta cheese, and its sensory properties. Twenty Ionica goats were randomly assigned to the following two groups (n = 10): the control received a traditional forage mixture (Avena sativa, 70%; Vicia sativa, 20%; Trifolium spp., 10%), while the experimental group was given Camelina sativa fresh forage (CAM). All of the dams grazed on pasture and received a commercial feed (500 g/head/day) at housing. The milk from the CAM group showed a higher (p < 0.05) content of dry matter, fat, lactose and concentrations of C6:0, C11:0, C14:0, C18:2 n-6, CLA and PUFA, while lower (p < 0.05) amounts of C12:0, C18:0 and saturated long chain FA (SLCFA). The Caciotta cheese from the CAM group showed a greater (p < 0.05) content of n-6 FA and n-6/n-3 ratio, although close to four, thus resulting adequate under the nutritional point of view. The overall liking, odour, taste, hardness, solubility and “goaty” flavour were better (p < 0.05) in the CAM cheeses. Further investigation would be advisable in order to evaluate the effect of feeding Camelina forage obtained from different phenological stages, and the application of ensiling techniques.