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 gamma-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 gamma-ray luminosity (for E = 0.26 to 10 TeV, distance d = 2 kpc) of L-gamma < 1.7 x 10(33) erg s(-1), and the total energy in corresponding accelerated protons, W-p < 1.6 x 10(50) erg are estimated ( for proton energies E-p similar to 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 E-p similar to 1 GeV to 3 PeV, assuming a differential particle index -2) gives W-P < 6.3 x 10(50) erg. A lower limit on the post-shock magnetic field of B > 25 G results when considering the synchrotron/inverse-Compton framework for the observed X-ray flux and gamma-ray upper limits.