We report the first \textit{ab initio} calculation of the nuclear-structure-dependent radiative correction \(\delta_{ \mathrm{NS} }\) to the \({}^{10}\mathrm{C} \rightarrow {}^{10}\mathrm{B}\) superallowed transition, computed with the no-core shell model and chiral effective field theory. We obtain \(\delta_{ \mathrm{NS} } = - 0.400 (29)_{ \mathrm{nuc} } (12)_{n,\mathrm{el} }\) with a \(1.7\)-times reduction in the nuclear uncertainty when compared to the current literature estimate based on the shell model and Fermi gas picture. This work paves the way for a precise determination of \(V_{ud}\) from superallowed beta decays.