The cross-section for prompt antiproton production in collisions of protons with an energy of \(6.5\) TeV incident on helium nuclei at rest is measured with the LHCb experiment from a data set corresponding to an integrated luminosity of \(0.5\,nb^{-1}\). The target is provided by injecting helium gas into the LHC beam line at the LHCb interaction point. The reported results, covering antiproton momenta between \(12\) and \(110\,\mathrm{GeV/}c\), represent the first direct determination of the antiproton production cross-section in \({\rm p He}\) collisions, and impact the interpretation of recent results on antiproton cosmic rays from space-borne experiments.