A search for light dark matter (LDM) will be performed by the DarkMESA experiment behind the electron beam-dump in the external beam-line of the MESA accelerator in Mainz, Germany. Various dark sector models motivate the existence of sub-GeV scalar and Majorana or pseudo-Dirac DM, that are accessible in this type of beam-dump experiments, e.g., by coupling to a dark photon mediator $A'$. In the presence of LDM in the dark sector with masses $m_\chi < m_{A'}/2$ and a dark coupling strength $\alpha_D \sim {\cal O}(O.1-1)$, the $A'$ would predominantly decay invisibly into $\chi\bar\chi$ particle pairs. The experiment makes use of the high intensity electron beam available at MESA and will run parasitically to the scheduled program for the external beam mode. The experiment is based on a solid and reliable detection technology and will collect an unprecedented accumulated charge in a few years time, that will extend current exclusion limits for LDM.