Young core-collapse supernovae with dense-wind progenitors may be able to accelerate cosmic-ray hadrons beyond the knee of the cosmic-ray spectrum , and this may result in measurable gamma-ray emission.We searched for gamma-ray emission from ten supernovae observed with the High Energy Stereoscopic System ( H.E.S.S . ) within a year of the supernova event . Nine supernovae were observed serendipitously in the H.E.S.S . data collected between December 2003 and December 2014 , with exposure times ranging from 1.4 hours to 53 hours . In addition we observed SN 2016adj as a target of opportunity in February 2016 for 13 hours . No significant gamma-ray emission has been detected for any of the objects , and upper limits on the > 1 TeV gamma-ray flux of the order of \sim 10 ^ { -13 } cm ^ { -2 } s ^ { -1 } are established , corresponding to upper limits on the luminosities in the range \sim 2 \times 10 ^ { 39 } erg s ^ { -1 } to \sim 1 \times 10 ^ { 42 } erg s ^ { -1 } . These values are used to place model-dependent constraints on the mass-loss rates of the progenitor stars , implying upper limits between \sim 2 \times 10 ^ { -5 } and \sim 2 \times 10 ^ { -3 } M _ { \odot } yr ^ { -1 } under reasonable assumptions on the particle acceleration parameters .