The measurement of charmonium states produced in proton-neon ( Formula omitted) collisions by the LHCb experiment in its fixed-target configuration is presented. The production of Formula omitted and Formula omitted mesons is studied with a beam of 2.5 Formula omitted protons colliding on gaseous neon targets at rest, corresponding to a nucleon-nucleon centre-of-mass energy Formula omitted. The data sample corresponds to an integrated luminosity of Formula omitted nb Formula omitted. The Formula omitted and Formula omitted hadrons are reconstructed in Formula omitted Formula omitted final states. The Formula omitted production cross-section per target nucleon in the centre-of-mass rapidity range Formula omitted is found to be Formula omitted. The ratio of Formula omitted and Formula omitted cross-sections is evaluated to Formula omitted. The Formula omitted to Formula omitted relative production rate is found to be Formula omitted in good agreement with other measurements involving beam and target nuclei of similar sizes.