  We investigate the scalar field perturbations of the 4+1-dimensional
Schwarzschild black hole immersed in a G\"{o}del Universe, described by the
Gimon-Hashimoto solution.This may model the influence of the possible rotation
of the Universe upon the radiative processes near a black hole. In the regime
when the scale parameter $j$ of the G\"{o}del background is small, the
oscillation frequency is linearly decreasing with $j$, while the damping time
is increasing. The quasinormal modes are damping, implying stability of the
Schwarzschild-G\"{o}del space-time against scalar field perturbations. The
approximate analytical formula for large multipole numbers is found.
