In this work we present a theoretical approach to deal with radiative decays of meson molecules. This is a promising framework to understand mesons that lie near the production threshold of $D$ and $B$ mesons, and don't fit in the traditional quarkonia predictions. We apply this approach specifically to the meson $X(3872)$: considering it a $D D^*$ molecule, we deal with its radiative decays $X \to J/ \psi$ and $ X \to \psi (2S)$. Contrary to previous claims, we demonstrate that the molecular model is compatible with the experimental radiative decay data. We use effective field theory techniques and the so called power-divergence subtraction (PDS) scheme. Based on the popular dimensional regularization and minimal subtraction scheme, PDS is designed to handle non-perturbative phenomena such as bound states and resonances. We find that short and long-distance physics are equally important in these decays. Our results may be used as guide to build models for the short-distance structure of the $X(3872)$.