Magnetization and muon spin rotation experiments were performed in La2−xBaxCuO4 (x = 1/8) as a function of hydrostatic pressure up to p ≃ 2.2 GPa. It was found that the magnetic volume fraction of the static stripe phase strongly decreases linearly with pressure, while the superconducting volume fraction increases by the same amount. This demonstrates competition between bulk superconductivity and static magnetic order in the stripe phase of La1.875Ba0.125CuO4 and that these phenomena occur in mutually exclusive spatial regions. The present results also reveal that the static spin-stripe phase still exists at pressures, where the long-range low-temperature tetragonal (LTT) structure is completely suppressed. This indicates that the long-range LTT structure is not necessary for stabilizing the static spin order in La1.875Ba0.125CuO4.