Abstract Measurements of the Epoch of Reionization (EoR) 21-cm signal hold the potential to constrain models of reionization. In this paper we consider a reionization model with three astrophysical parameters namely (1) the minimum halo mass which can host ionizing sources, Mmin, (2) the number of ionizing photons escaping into the IGM per baryon within the halo, Nion and (3) the mean free path of the ionizing photons within the IGM, Rmfp. We predict the accuracy with which these parameters can be measured from future observations of the 21-cm power spectrum (PS) using the upcoming SKA-Low. Unlike several earlier works, we account for the non-Gaussianity of the inherent EoR 21-cm signal. Considering cosmic variance only and assuming that foregrounds are completely removed, we find that non-Gaussianity increases the volume of the 1σ error ellipsoid of the parameters by a factor of 133 relative to the Gaussian predictions, the orientation is also different. The ratio of the volume of error ellipsoids is 1.65 and 2.67 for observation times of 1024 and 10000 hours respectively, when all the k modes within the foreground wedge are excluded. With foreground wedge excluded and for 1024 hours, the 1D marginalized errors are (ΔMmin/Mmin, ΔNion/Nion, ΔRmfp/Rmfp) = (6.54, 2.71, 7.75) × 10−2 which are respectively $2 \%$, $5 \%$ and $23 \%$ larger than the respective Gaussian predictions. The impact of non-Gaussianity increases for longer observations, and it is particularly important for Rmfp.