In the Standard Model (SM) the branching ratio for the decay K_L \to \nu \bar{\nu} into two neutrinos is helicity suppressed and predicted to be very small \leq O(10^{-17}). We consider two natural extensions of the SM, such as two-Higgs-doublet model (2HDM) and the \nuMSM with additional singlet scalar, those main features is that they can lead to an enhanced Br(K_L \to invisible). In the 2HDM the smallness of the neutrino mass is explained due to the smallness of the second Higgs doublet vacuum expectation value. Moreover, the \nuMSM extension with additional singlet field can explain the (g - 2) muon anomaly. The considered models demonstrate that the K_L \to invisible decay is a clean probe of new physics scales well above 100 TeV, that is complementary to rare K \to \pi+invisible decay, and provide a strong motivation for its sensitive search in a near future low-energy experiment.