We report the direct measurement of isotope shifts of the barium $6s^2$ ${}^1{S}_0\text{–}5d6p^3{D}_1^{\mathrm{o}}$ 413-nm electric quadrupole transition, which is utilized for efficient barium ion trapping via photoionization using a single coherent light source. The measured isotope shifts relative to ${}^{138}\mathrm{Ba}$ are $392.9\text{ifmmode}\pm \text{else}\text{textpm}\text{fi}0.9\mathrm{MHz}$, $178.1\text{ifmmode}\pm \text{else}\text{textpm}\text{fi}0.8\mathrm{MHz}$, $401.4\text{ifmmode}\pm \text{else}\text{textpm}\text{fi}1.2\mathrm{MHz}$, and $124.3\text{ifmmode}\pm \text{else}\text{textpm}\text{fi}1.3\mathrm{MHz}$ for isotopes with atomic numbers 137, 136, 135, and 134, respectively. We verify the measured isotopes with King plot analysis and compare the result with the formerly known shifts inferred from previous studies on neighboring transitions. The results can be used for efficient isotope selective loading of low-abundant barium ions, while careful suppression of line broadening is required for successful isotopic selectivity.