We report on measurements of the magnetic moment in superconducting MgB<sub>2sub> single crystals by SQUID magnetometry. Neutron irradiation is employed to modify the defect structure. We show that both the reversible as well as the irreversible properties are significantly affected by irradiation. The upper critical field and the irreversibility line are strongly enhanced for H<sub>asub>c and the critical current density shows a very pronounced fishtail.