For the Fermi-Hubbard model in the strongly interacting Mott insulator state, we study the prethermalization dynamics after a quench (switching on the hopping rate). To this end, we employ the method of the hierarchy of correlations and compare different levels of accuracy. To leading order, the usual free quasiparticle dynamics (as encoded in the two-point correlation functions) yields the standard picture of prethermalization. Taking into account the back-reaction of these quasiparticle fluctuations onto the mean-field background as the first next-to-leading-order effect, we observe a strong degradation of prethermalization, especially in low dimensions. In contrast, the inclusion of three-point correlations enhances prethermalization.