Here we present the effect of uniaxial stress on the magnetic stripes in the cuprate system La$_{2-x}$Ba$_{x}$CuO$_4$ with $x = 0.115$, previously found to have a stress-induced enhancement in the superconducting transition temperature. By means of neutron scattering, we show that the static stripes are suppressed by stress, pointing towards a trade-off between superconductivity and static magnetism, in direct agreement with previously reported $\mu$SR measurements. Additionally, we show that some of the reduced weight in the elastic channel appears to have moved to the inelastic channel. Moreover, a stress-induced momentum shift of the fluctuations towards the typical 1/8 value of commensurability is observed. These results impose a strong constraint on the theoretical interpretation of stress-enhanced superconductivity in cuprate systems.