Harmonic ac susceptibilities, χ_n = χ_n' + i χ_n'', and ac magnetization of a metallic granular superconductor of MgB₂ have been measured as a function of temperature, ac field amplitude and additional small dc field in the temperature range between 15 and 45 K. Temperature- and amplitude-dependent measurements are similar to those obtained for a typical high-temperature superconductor. In addition, MgB₂ has a very narrow transition temperature width and high critical current densities. The experimental results have been compared to the numerical solutions of a model based on Bean's critical state. Odd harmonic susceptibilities (n = 3, 5 and 7) are in good agreement with those obtained numerically from the model. In contrast, the measured even harmonic susceptibilities exhibit a peak-like behaviour below T_c, with only small magnitudes of about 10⁻⁴ (SI). The results are interpreted in terms of flux penetration to the bulk of superconductor MgB₂.