Magnetization of Eu_0.58Sr_0.42MnO₃ was measured under hydrostatic pressures up to 0.8 GPa in order to investigate the effect of pressure on the metal-insulator transition, which was investigated at high pressure by resistivity measurements. At ambient pressure, below about 45 K, the magnetization vs temperature curve reveals a spin-glass behavior as reported for a previous experiment. With increasing pressure, the magnetization increases at both 0.005 T and 0.5 T, and a cluster-glass behavior appears at 0.5 T above 0.37 GPa. On the other hand, the magnetization increases with increasing pressure at 1.5 T and 5.0 T. We also found that the high-field susceptibility increases linearly with increasing pressure at a rate of (dχ_hf/dp) = 0.0336(6)μ_BT^-1 GPa^-1.