The effect of high pressure exceeding 6 GPa on magnetism and multiferroicity was investigated for the olivine Mn2GeO4 that shows successive magnetic transitions at ambient pressure and a ferroelectric ground state driven by spin- spiral order. We measured heat capacity, dielectric constant, and electric polarization at various pressures using a diamond anvil cell. The pressure evolution of the magnetic structures was also investigated by powder neutron diffraction measurements using a Paris- Edinburgh press. We found that all of the magnetic transition temperatures are enhanced monotonically by applying pressure. Furthermore, the spin- driven ferroelectricity persists up to about 6 GPa but suddenly vanishes by 6.3 GPa. A consistent description of all data is achieved if an incommensurate- commensurate phase transition occurs with pressurization and causes the suppression of ferroelectricity. We discuss the origin of the observed pressure effects on the magnetism and multiferroicity in Mn2GeO4 in terms of a pressure- induced change in the superexchange magnetic interactions.