The invention relates to the field of medicine, in particular to nanomedicine, which uses biodegradable nanospheres and microspheres to include biologically active proteins in their composition to stabilize their structure. This method provides for the preliminary inclusion of a histone of animal origin in the composition of the matrix of nanospheres with a diameter of not more than 1000 nm, which are obtained on the basis of dextran, and the subsequent inclusion of the histone-containing nanospheres into the resorbable microspheres, which are prepared on the basis of the polylactide-glycolide copolymer. Extraction of histone from the resorbed microspheres takes place for at least 50 days. The provided invention ensures preservation of the native structure of the protein due to its inclusion in the composition of polymeric nanospheres, and increases the reliability and simplifies the method of obtaining native protein in the composition of polymeric nanospheres and resorbable microspheres that are intended to prolong the physiological action of native protein used for therapeutic purposes.