The effect of urine chemosignals of domestic male cats (Felis catus L.) on the stability of the bone marrow cell genome and corticosterone level in blood plasma of recipient mice (Mus musculus L.) is studied. It is demonstrated that a two-hour sniffing of volatile chemosignals leads to an increase in the frequency of bone marrow cells with damaged DNA, while 24 h exposure to chemosignals leads to an increase of chromosomal aberrations frequency in these cells. Thus, the effect of genomic instability induction in bone marrow cells of house mice by predator’s chemosignals is for the first time demonstrated in the work. At the same time, no increase in the corticosterone level is detected in the blood plasma either 30 or 60 min after the beginning of the exposure to the chemosignals of cat urine (CU). The physiological factors contributing to DNA damages accumulation in bone marrow cells, as well as the long-term consequences of the effect of these chemosignals on the genome stability, are discussed.