  We study a Fermionic chain with nearest-neighbor hopping and density-density
interactions, where the nearest-neighbor interaction term is driven
periodically. We show that such a driven chain exhibits prethermal strong
Hilbert space fragmentation (HSF) in the high drive amplitude regime at
specific drive frequencies $\omega_m^{\ast}$. This constitutes the first
realization of HSF for out-of-equilibrium systems. We obtain analytic
expressions of $\omega_m^{\ast}$ using a Floquet perturbation theory and
provide exact numerical computation of entanglement entropy, equal-time
correlation functions, and the density autocorrelation of Fermions for finite
chains. All of these quantities indicate clear signatures of strong HSF. We
study the fate of the HSF as one tunes away from $\omega_m^{\ast}$ and discuss
the extent of the prethermal regime as a function of the drive amplitude.
