We demonstrate that the anomalous ionization rate observed in the Central Molecular Zone can be attributed to MeV dark matter annihilations into e+e- pairs for galactic dark matter profiles with slopes γ>1. The low annihilation cross sections required avoid cosmological constraints and imply no detectable inverse Compton, bremsstrahlung, or synchrotron emission in radio, x- and γ rays. The possible connection with the source of the unexplained 511 keV line emission in the Galactic Center suggests that both observations could be correlated and have a common origin.