We study magnetohydrodynamic (MHD) standing shocks in ingoing plasmas in a black hole (BH) magnetosphere. We find that low or mid latitude (non-equatorial) standing MHD shocks are both physically possible, creating very hot and/or magnetized plasma regions close to the event horizon. We also investigate the effects of the poloidal magnetic field and the BH spin on the properties of shocks and show that both effects can quantitatively affect the MHD shock solutions. MHD shock formation can be a plausible mechanism for creating high energy radiation region above an accretion disk in AGNs.