Zeolites, especially clinoptilolites, have wide application in removing heavy metals from different solutions and wastewater. The detoxification capacity of the clinoptilolite sorbent KLS-10-MA, a modified natural Bulgarian zeolite, applied as a food supplement in conditions of an ecotoxicological experiment with conventional food and lead was demonstrated for the first time. Laboratory mice, inbred imprinting control region strain, were used in a 90-day ecotoxicological experiment. Animals were divided into four experimental groups. Lead bioaccumulations in exposed and non-supplemented/supplemented with KLS-10-MA animals were compared. As additional control, healthy animals non-exposed to Pb were fed with conventional forage mixed with 12.5% KLS-10-MA. The dietary inclusion of the sorbent reduced Pb concentrations in exposed and supplemented mice by 84%, 89%, 91%, 77%, and 88% in carcass, liver, kidneys, bones, and feces, respectively. A mathematical model was proposed to outline the common trends of bone Pb bioaccumulation in exposed and non-supplemented/supplemented animals. Characteristic parameters of the kinetics of Pb concentrations were determined. Based on the model, the coefficient of absorption of Pb by gastrointestinal mucosa in the supplemented mice was found-η = 3.53% (versus η = 15% in non-supplemented ones). The present study clearly indicates that there is a realistic perspective to create a new drug based on modified natural clinoptilolites in cases of chronic heavy metal intoxication, without negatively affecting the environment.