We have recently proposed that the Standard Model Higgs might be responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In this paper we study the level of non-Gaussianity in the cosmological perturbations which are inevitably generated due to the non-linearities of the Standard Model Higgs potential. In particular, for the current central value of the top mass, we find that a future detection of non-Gaussianity would exclude the detection of tensor modes by the PLANCK satellite.