We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using molecular dynamics simulations. We compute the self-van Hove correlation function Gs(r, t), and self-intermediate scattering function Fs(k, t) and compare these functions with those obtained from mean-squared displacement MSD using the Gaussian approximation. According to this approximation, a linear MSD with time implies a Gaussian behavior for Gs(r, t) and Fs(k, t) at all times. Surprisingly, we find that these functions deviate from Gaussian at intermediate time scales, indicating the failure of the Gaussian approximation. Furthermore, we quantify these deviations by the non-Gaussian parameter, and we find that the deviations increase with decreasing the temperature of the liquid. The origin of the non-Gaussian behavior may be the heterogeneous dynamics of dust particles observed in 2D Yukawa liquids.