We study the process $e^+e^-\to e^+e^- \eta'$ in the double-tag mode and measure for the first time the $\gamma^{\star}\gamma^{\star} \to \eta'$ transition form factor $F_{\eta'}(Q_1^2, Q_2^2)$ in the momentum-transfer range \mbox{2 $<Q_1^2, Q_2^2<$ 60 GeV$^2$}. The analysis is based on a data sample corresponding to an integrated luminosity of around 469 fb$^{-1}$ collected at the PEP-II $e^+e^-$ collider with the BaBar detector at center-of-mass energies near 10.6 GeV.