Puppis A is an interesting ~4 kyr-old supernova remnant (SNR) that shows strong evidence of interaction between the forward shock and a molecular cloud. It has been studied in detail from radio frequencies to high-energy (HE, 0.1-100 GeV) gamma-rays. An analysis of the Fermi-LAT data has shown an extended HE gamma-ray emission with a 0.2-100 GeV spectrum exhibiting no significant deviation from a power law, unlike most of the GeV-emitting SNRs known to be interacting with molecular clouds. This makes it a promising target for imaging atmospheric Cherenkov telescopes (IACTs) to probe the gamma-ray emission above 100 GeV. Very-high-energy (VHE, E >= 0.1 TeV) gamma-ray emission from Puppis A is for the first time searched for with the High Energy Stereoscopic System (H.E.S.S.). The analysis of the H.E.S.S. data does not reveal any significant emission towards Puppis A. The derived upper limits on the differential photon flux imply that its broadband gamma-ray spectrum must exhibit a spectral break or cutoff. By combining Fermi-LAT and H.E.S.S. measurements, the 99% confidence level upper limits on such a cutoff are found to be 450 and 280 GeV, assuming a power law with a simple exponential and a sub-exponential cutoff, respectively. It is concluded that none of the standard limitations (age, size, radiative losses) on the particle acceleration mechanism, assumed to be still on-going at present, can explain the lack of VHE signal. The scenario in which particle acceleration has ceased some time ago is considered as an alternative explanation. The HE/VHE spectrum of Puppis A could then exhibit a break of non-radiative origin, (as observed in several other interacting SNRs, albeit at somewhat higher energies) owing to the interaction with dense and neutral material in particular towards the northeastern region.
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