We consider the decoupling of neutrinos in the early Universe in presence of non-standard neutral current neutrino-electron interactions (NSI). We first discuss a semi-analytical approach to solve the relevant kinetic equations and then present the results of fully numerical and momentum-dependent calculations, including flavor neutrino oscillations. We present our results in terms of both the effective number of neutrino species (Neff) and the impact on the abundance of He-4 produced during Big Bang Nucleosynthesis. We find that, for NSI parameters within the ranges allowed by present laboratory data, non-standard neutrino-electron interactions do not essentially modify the density of relic neutrinos nor the bounds on neutrino properties from cosmological observables, such as their mass. Nonetheless, the presence of neutrino-electron NSI may enhance the entropy transfer from electron-positron pairs into neutrinos instead of photons, up to a value of Neff=3.12. This is almost three times the correction to Neff=3 that appears for standard weak interactions.