Abstract : A search for a very-high-energy (VHE; >= 100 GeV) gamma-ray signal from self-annihilating particle Dark Matter (DM) is performed towards a region of projected distance r ~ 45-150 pc from the Galactic Center. The background-subtracted gamma-ray spectrum measured with the High Energy Stereoscopic System (H.E.S.S.) gamma-ray instrument in the energy range between 300 GeV and 30 TeV shows no hint of a residual gamma-ray flux. Assuming conventional Navarro-Frenk-White (NFW) and Einasto density profiles, limits are derived on the velocity-weighted annihilation cross section < \sigma v> as a function of the DM particle mass. These are among the best reported so far for this energy range. In particular, for the DM particle mass of ~1 TeV, values for <\sigma v> above 3 * 10^(-25) cm^3 s^(-1) are excluded for the Einasto density profile. The limits derived here differ much less for the chosen density profile parametrizations, as opposed to limits from gamma-ray observations of dwarf galaxies or the very center of the Milky Way, where the discrepancy is significantly larger.