The results of investigation of the structure and magnetic properties of an undoped monocrystal and a weakly doped polycrystalline zinc oxide ceramics are presented. The degree of defectiveness of the monocrystal is evaluated. It is shown that the existence of vacancies and atoms of zinc in interstices of the crystal lattice with concentration n ≈ 10^–21 cm^–3 does not lead to the emergence of any ferromagnetic properties in the investigated samples.