In this paper we report the generation of higher harmonics in a bulk polycrystalline MgB₂ superconductor when it is subjected to ac and dc magnetic field. The MgB₂ sample shows the generation of higher odd harmonics when an ac field is applied. The application of a small dc field (~few gauss) in addition to an ac field also leads to the generation of second and fourth harmonics, which is an indication of the presence of some weak link grain boundaries in a MgB₂ superconductor. We have studied the variation of the amplitude of higher harmonics with temperature for different values of amplitude of ac field. The observed results are interpreted in terms of weak link grain boundaries and a critical state model.