The presence of massive neutrinos in cosmology induces a scale-dependent suppression of structure formation that is strongest on small scales. Measuring this suppression is a key component towards constraining neutrino masses from cosmological data, and is one of the main goals of ongoing and future surveys like eBOSS, DES, LSST, Euclid or DESI. Studies of the clustering of the Lyman-alpha (Lya) forest provide a precise measurement of the linear power on small scales, and in combination with CMB data they provide some of the tightest constraints on the sum of the neutrino masses. I will present results from a set of hydrodynamical simulations studying the effect of massive neutrinos on the clustering of the Lya forest and show that the Lya forest alone cannot distinguish between the effect of massive neutrinos and a change in the amplitude of primordial fluctuations at the 1% level. I conclude that given the precision of current and near-term measurements of the Lya forest, it is not necessary to include massive neutrinos in Lya forest analysis; either in the simulations or as a parameter in the likelihood.