A relativistic kinetic description for the irreversible thermodynamic process of gravitationally induced particle production is proposed in the context of an expanding Friedmann-Robertson-Walker (FRW) geometry. We show that the covariant thermodynamic treatment referred to as "adiabatic" particle production provoked by the cosmic time-varying gravitational field has a consistent kinetic counterpart. The variation of the distribution function is associated to a non-collisional kinetic term of quantum-gravitational origin which is proportional to the ratio $\Gamma/H$, where $\Gamma$ is the gravitational particle production rate and H is the Hubble parameter. For $\Gamma << H$ the process is negligible and as should be expected it also vanishes (regardless of the value of $\Gamma$) in the absence of gravitation. The resulting non-equilibrium distribution function has the same functional form of equilibrium with the evolution laws corrected by the particle production process. The macroscopic temperature evolution law is also kinetically derived for massive and massless particles. The present approach points to the possibility of an exact (semi-classical) quantum-gravitational kinetic treatment by incorporating back-reaction effects in the cosmic background.