We present a novel method to infer the Dark Matter (DM) content and spatial distribution within galaxies, based on convolutional neural networks trained within state-of-the-art hydrodynamical simulations (Illustris TNG100). The framework we have developed is capable of inferring the DM mass distribution within galaxies of mass $~10^{11}-10^{13}M_{\odot}$ with very high performance from the gravitationally baryon dominated internal regions to the DM-rich, baryon-depleted outskirts of the galaxies. With respect to traditional methods, the one presented here also possesses the advantages of not relying on a pre-assigned shape for the DM distribution, to be applicable to galaxies not necessarily in isolation, and to perform very well even in the absence of spectroscopic observations