New physics beyond the Standard Model is required to give mass to the light neutrinos. One of the simplest ideas is to introduce new heavy, gauge singlet fermions that play the role of right-handed neutrinos in a seesaw mechanism. They could have large Yukawa couplings to the Higgs boson, affecting the Higgs couplings and in particular the triple Higgs coupling $\lambda_{HHH}^{}$, the measure of which is one of the major goals of the LHC and of future colliders. We present a study of the impact of these heavy neutrinos on $\lambda_{HHH}^{}$ at the one-loop level, first in a simplified 3+1 model with one heavy Dirac neutrino and then in the inverse seesaw model. Taking into account all possible experimental constraints, we find that sizeable deviations of the order of 35% are possible, large enough to be detected at future colliders, making the triple Higgs coupling a new, viable observable to constrain neutrino mass models. The effects are generic and are expected in any new physics model including TeV-scale fermions with large Yukawa couplings to the Higgs boson, such as those using the neutrino portal.