Primordial black holes could have been formed in the early universe from sufficiently large cosmological perturbations re-entering the horizon when the Universe is still radiation dominated. These originate from the spectrum of curvature perturbations generated during inflation at small-scales. Because of the non-linear relation between the curvature perturbation ζ and the overdensity δρ, the formation of the primordial black holes is affected by intrinsic non-Gaussianity even if the curvature perturbation is Gaussian. We investigate the impact of this non-Gaussianity on the critical threshold δc which measures the excess of mass of the perturbation, finding a relative change with respect to the value obtained using a linear relation between ζ and δρ, of a few percent suggesting that the value of the critical threshold is rather robust against non-linearities. The same holds also when local primordial non-Gaussianity, with fNL≳−3/2, are added to the curvature perturbation.