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 GeV/c, represent the first direct determination of the antiproton production cross section in p-He collisions, and impact the interpretation of recent results on antiproton cosmic rays from space-borne experiments.