Context. The Metis coronagraph is one of the remote sensing instruments hosted on board the ESA/NASA Solar Orbiter mission. Metis is devoted to carry out the first simultaneous imaging of the solar corona in both visible light (VL) and ultraviolet (UV). High-energy particles can penetrate spacecraft materials and may limit the performance of the on-board instruments. A study of the galactic cosmic-ray (GCR) tracks observed in the first VL images gathered by Metis during the commissioning phase is presented here. A similar analysis is planned for the UV channel. Aims. We aim to formulate a prediction of the GCR flux up to hundreds of GeV for the first part of the Solar Orbiter mission to study the performance of the Metis coronagraph. Methods. The GCR model predictions are compared to observations gathered on board Solar Orbiter by the High-Energy Telescope in the range between 10 MeV-100 MeV in the summer of 2020 as well as with the previous measurements. Estimated cosmic-ray fluxes above 70 MeV n−1 have been also parameterized and used for Monte Carlo simulations aimed at reproducing the cosmic-ray track observations in the Metis coronagraph VL images. The same parameterizations can also be used to study the performance of other detectors. Results. By comparing observations of cosmic-ray tracks in the Metis VL images with FLUKA Monte Carlo simulations of cosmic-ray interactions in the VL detector, we find that cosmic rays fire only a fraction, on the order of 10−4 , of the whole image pixel sample. We also find that the overall efficiency for cosmic-ray identification in the Metis VL images is approximately equal to the contribution of Z>2 GCR particles. A similar study will be carried out during the whole of the Solar Orbiter’s mission duration for the purposes of instrument diagnostics and to verify whether the Metis data and Monte Carlo simulations would allow for a long-term monitoring of the GCR proton flux.