The study aimed to determine the content of 17 elements (Al, As, Ba, Cd, Co, Cr, Cu, Fe, Li, Mn, Mo, Ni, Pb, Sb, Se, Sr, and Zn) in samples of sheep milk, cheese, and whey (36 samples in total) collected from a farm in an environmentally burdened area due to the long-term mining and industrial activity in Slovakia as well as to determine the possible risk of consumption via health risk assessment calculations. Consumption of 120 g of milk, 500 g of milk, 20 g of cheese, and 100 g of cheese were used in calculations for children and adults, respectively. According to the results, concentrations of four elements are controversial. Lead concentrations in all types of samples exceeded the maximum permissible lead limit in milk set by European Union legislation. The content of Se and As is problematic for children’s consumption, and the target hazard quotient for As and Al is higher than one (considered potentially not safe) in all scenarios. According to the target system approach, lead concentrations in milk and cheese could adversely influence the nervous system and kidneys of adults’ and children’s developmental and reproductive systems. Considering the worst-case scenario, consuming sheep milk and cheese from the monitored areas could represent a risk and be potentially harmful to human health, mainly for children. However, further monitoring of the levels of elements and concentrations in environmentally burdened areas and more robust data on consumption are needed.