The first measurement of heavy-flavour production by the LHCb experiment in its fixed-target mode is presented. The production of $J/psi$ and $D^0$ mesons is studied with beams of protons of different energies colliding with gaseous targets of helium and argon with nucleon-nucleon centre-of-mass energies of $sqrt{s_{NN}} = 86.6 $ and $ 110.4$ ${rm GeV}$, respectively. The $J/psi$ and $D^0$ (including charge conjugate) production cross sections in $p{rm He}$ collisions in the rapidity range $[2,4.6]$ are found to be $sigma_{J/psi} = 652 pm 33$ (stat) $pm 42$ (syst) nb$/$nucleon and $sigma_{D^0} = 80.8 pm 2.4$ (stat) $pm 6.3$ (syst) $mu$b$/$nucleon, where the first uncertainty is statistical and the second is systematic. No evidence for a substantial intrinsic charm content of the nucleon is observed in the large Bjorken-$x$ region.
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