Using x-ray absorption spectroscopy, wehave studied the effect of pressure on femtometer-scale bond strain due to anisotropic magnetostriction in a thin FeCo film. At 7 GPa local magnetostrictive strain is found to be larger than at ambient, in agreement with spin-polarized ab initio electronic structure calculations, but contrary to the expected effect of compression on bond stiffness. The availability of high pressure data on local magnetostrictive strain opens new capabilities for validating theoretical predictions and can lead to the development of materials with the desired properties.