In accordance with the second principle of thermodynamics, periodic drives generically lead to heating, i.e. an increase in energy and entropy. A fundamental question is under which conditions this heating process can be made slow. Motivated by recent theoretical works on Floquet quantum systems, we discovered a new mechanism that can reduce exponentially the heating rate of a generic interacting system. This scenario, which we termed “statistical prethermalization”, has a broad range of applications in real physical systems, in both the quantum and classical world.