We compute the quasinormal frequencies for scalar and electromagnetic perturbations of an improved Schwarzschild geometry in the framework of asymptotically safe gravity, which is one of the approaches to quantum gravity. Adopting the widely used WKB semi-classical approximation, we investigate the impact on the spectrum of the angular degree, the overtone number as well as the black hole mass. We summarize our numerical results in tables, and for better visualization, we show them graphically as well. All modes are found to be stable. Finally, we compare our numerical results with those corresponding to the classical Schwarzschild solution as well as to the results obtained using a different approach. Our findings show that i) a different cut-off identification does not affect the spectra significantly, and ii) for hypothetical objects with masses comparable to the Planck mass, the difference in the numerical values between the modes of the classical solution and the modes of the improved solution studied here is of the order of a few per cent. On the contrary, for realistic, astrophysical BHs no difference in the frequencies is observed.