The difference in the mean-square nuclear charge radius of xenon isotopes was measured utilizing a method based on extreme ultraviolet spectroscopy of highly charged Na-like ions. The isotope shift of the Na-like 1 (3 - 3) transition between the Xe and Xe isotopes was experimentally determined using the electron-beam ion-trap facility at the National Institute of Standards and Technology. The mass-shift and the field-shift coefficients were calculated with enhanced precision by the relativistic many-body perturbation theory and multiconfiguration Dirac-Hartree-Fock method. The mean-square nuclear charge radius difference was found to be 〈〉 = 0.269(42) fm. Our result has smaller uncertainty than previous experimental results and agrees with the literature values.