Aims.Observations of Kepler’s supernova remnant (G4.5+6.8) with the H.E.S.S. telescope array in 2004 and 2005 with atotal live time of 13 hare presented.Methods.Stereoscopic imaging of Cherenkov radiation from extensive air showers is used to reconstruct the energy and directionof the incidentgamma rays.Results.No evidence for a very high energy (VHE:>100 GeV) gamma-ray signal from the direction of the remnant is found. An upper limit (99%confidence level) on the energy flux in the range 230 GeV−12.8 TeV of 8.6×10−13erg cm−2s−1is obtained.Conclusions.In the context of an existing theoretical model for the remnant, the lack of a detectable gamma-ray flux implies a distanceof at least6.4 kpc. A corresponding upper limit for the density of the ambient matter of 0.7 cm−3is derived. With this distance limit, and assuming a spectralindexΓ=2, the total energy in accelerated protons is limited toEp<8.6×1049erg. In the synchrotron/inverse Compton framework, extrapolatingthe power law measured by RXTE between 10 and 20 keV down in energy, the predicted gamma-ray flux from inverse Compton scattering isbelow the measured upper limit for magnetic field values greater than 52μG.