We investigate dynamical stability of the ground state against a time-periodic and spatially-inhomogeneous magnetic field for finite quantum XXZ spin chains. We use the survival probability as a measure of stability and demonstrate that it decays as P(t) ∝ t-1/2 under a certain condition. The dynamical properties should also be related to the level statistics of the XXZ spin chains with a constant spatially-inhomogeneous magnetic field. The level statistics depends on the anisotropy parameter and the field strength. We show how the survival probability depends on the anisotropy parameter, the strength and frequency of the field.