The HESS array of Cherenkov telescopes has performed, from 2004 to 2007, a survey of the inner galactic plane at photon energies above 100 GeV. About 400 hours of data have been accumulated in the region between -30 and +60degrees in galactic longitude, and between -3 and +3degrees in galactic latitude. Assuming that dark matter is composed of weakly interacting massive particles, we calculate here the HESS sensitivity map for dark matter annihilations, and derive the first experimental constraints on the ("minispikes") scenario, in which a gamma-ray signal arises from dark matter annihilation around intermediate mass black holes. The data exclude the proposed scenario at a 90% confidence level for dark matter particles with velocity-weighted annihilation cross section σv above 10-28cm3s-1 and mass between 800 GeV and 10 TeV.