Dark Matter (DM) existence is a milestone of the cosmological standard model and, yet its nature remains a complete mystery. In this contribution, we investigate an original way to probe the properties of sub-GeV DM particle candidates, by exploiting the cosmic-ray (CR) transport inside starburst nuclei (SBNi). Indeed, SBNi are considered CR reservoirs, thereby being able to trap CRs for $\sim 10^5\, \rm yr$ years up to $\sim$ PeVs energies, leading to copious production of gamma-rays and neutrinos. As a result, interactions between DM and protons might indelibly change CR transport in these galaxies, perturbing the gamma-rays and neutrino production. We show that current gamma-ray observations from the M82 and the NGC 253, local starburst galaxies, pose strict limits on the elastic cross section down to $\sigma_{\chi p}\simeq 10^{-34} \rm cm^2$for DM masses $m_{\chi}\le 10^{-3}\, \rm MeV$. Furthermore, the current bounds have considerable room for improvement with the future gamma-ray measurements in the 0.1-10 TeV range from the Cherenkov Telescope Array up to $\sim 2$ orders of magnitude.