Using 3D radiation-hydrodynamical simulations, we study the effects of ionizing radiation on the formation of second-generation (SG) stars in globular clusters (GCs) with multiple stellar populations. In particular, we focus on massive ($10^7 \, \mathrm{M}_{\odot }$) and young (40-Myr old) GCs. We consider stellar winds from asymptotic giant branch (AGB) stars, ram pressure, gas accretion on to the cluster, and photo-ionization feedback of binary stars. We find that the stellar luminosity is strong enough to warm and ionize the intracluster medium, but it does not lead to a significant gas expulsion. The cluster can thus retain the ejecta of AGB stars and the accreted pristine gas. In addition, efficient cooling occurs in the central region of the cluster within $50\, \mathrm{Myr}$ from the formation of first generation stars, leading to the formation of SG stars. Our results indicate that the inclusion of photo-ionization does not suppress SG formation, but rather delays it by about $\sim 10\, \mathrm{Myr}$. The time delay depends on the density of the pristine gas, so that a denser medium exhibits a shorter delay in star formation. Moreover, photo-ionization leads to a modest decrease in the total SG mass, compared to a model without it.