The detection of gamma -rays from the source HESS J1745-290 in the Galactic Center (GC) region with the HESS array of Cherenkov telescopes in 2004 is presented. After subtraction of the diffuse gamma -ray emission from the GC ridge, the source is compatible with a point-source with spatial extent less than 1.2'(stat.) (95% CL). The measured energy spectrum above 160 GeV is compatible with a power-law with photon index of 2.25 +/- 0.04 (stat.) +/- 0.10 (syst.) and no significant flux variation is detected. These measurements are discussed in the framework of dark matter annihilation. It is found that the bulk of the VHE emission must have non-dark-matter origin. Loose constraints on the velocity-weighted annihilation cross section < sigma * v> are derived assuming the presence of an astrophysical non-dark-matter gamma -ray contribution.