We study an energy relaxation process after many degrees of freedom are excited in a Hamiltonian system with a large number of degrees of freedom. Bottlenecks of relaxation, where the relaxation of the excited elements is drastically slowed down, are discovered. By defining an internal state for the excited degrees of freedom, it is shown that the drastic slowing down occurs when the internal state is in a critical state. The relaxation dynamics brings the internal state into the critical state, and the critical bottleneck of relaxation is self-organized.