Observations of the shell-type supernova remnant SN1006 have been carried out with the HESS system of Cherenkov telescopes during 2003 (18.2 h with two operating telescopes) and 2004 (6.3 h with all four telescopes). No evidence for TeV γ-ray emission from any compact or extended region associated with the remnant is seen and resulting upper limits at the 99.9% confidence level are up to a factor 10 lower than previously-published fluxes from CANGAROO. For SN1006 at its current epoch of evolution we define limits for a number of important global parameters. Upper limits on the γ-ray luminosity (for E = 0.26 to 10 TeV, distance d = 2 kpc) of Lγ < 1.7 × 1033 erg s-1, and the total energy in corresponding accelerated protons, Wp<1.6 × 1050 erg are estimated (for proton energies Ep ̃ 1.5 to 60 TeV and assuming the lowest value n=0.05 cm-3 of the ambient target density discussed in literature). Extending this estimate to cover the range of proton energies observed in the cosmic ray spectrum up to the knee (we take here Ep ̃ 1 GeV to 3 PeV, assuming a differential particle index -2) gives Wp<6.3 × 1050 erg. A lower limit on the post-shock magnetic field of B>25 μG results when considering the synchrotron/inverse-Compton framework for the observed X-ray flux and γ-ray upper limits.