Employing the method of Wigner functions on curved spaces, we study classical kinetic (Boltzmann-like) equations of distribution functions for a real scalar field with the Lifshitz scaling. In particular, we derive the kinetic equation for z=2 on general curved spaces and for z=3 on spatially flat spaces under the projectability condition N=N(t), where z is the dynamical critical exponent and N is the lapse function. We then conjecture a form of the kinetic equation for a real scalar field with a general dispersion relation in general curved geometries satisfying the projectability condition, in which all the information about the nontrivial dispersion relation is included in the group velocity and which correctly reproduces the equations for the z=2 and z=3 cases as well as the relativistic case. The method and equations developed in the present paper are expected to be useful for developments of cosmology in the context of Hořava-Lifshitz gravity.