Recent observations of the Galactic center with ground based gamma-ray instruments ( CANGAROO-II , VERITAS , H.E.S.S . ) have revealed a TeV ( 10 ^ { 12 } eV ) gamma-ray signal consistent with the position of Sgr A* . The derived luminosity of the signal above 1 TeV is a few 10 ^ { 34 } ~ { } \mathrm { erg } \mathrm { s } ^ { -1 } which is slightly more than e.g . the gamma-ray luminosity of the Crab nebula and a plausible identification could be a conventional albeit strong gamma-ray source . The observations with the H.E.S.S . system of Cherenkov telescopes have decreased the solid angle subtended by the error box by more than a factor of hundred with respect to the previous observations of the VERITAS and CANGAROO groups . After studying the observed energy spectrum and angular distribution of the excess as seen by the H.E.S.S . experiment , a massive Dark Matter candidate with a minimum mass of 12 TeV ( 90 % c.l . ) and an upper limit on the WIMP density for r < 10 pc of 1261 ~ { } M _ { \odot } \mathrm { pc } ^ { -3 } \times \left ( \langle \sigma v \rangle / 3 \cdot 10 % ^ { -26 } \mathrm { cm } ^ { 3 } \mathrm { s } ^ { -1 } \right ) ^ { -1 / 2 } is required to explain the observed flux by an annihilation signal . The angular distribution of the excess events is consistent with a cuspy profile with \rho ( r ) \propto r ^ { - \alpha } with \alpha > 1.0 at a confidence level of 90 % . Even though the mass and the cross section of the Dark Matter constituents are unexpectedly high in the framework of most models of nonbaryonic Dark Matter , it can not be ruled out .