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). Highenergy particles penetrate spacecraft materials and may limit the performance of on-board instruments. A study of galactic cosmic-ray (GCR) tracks observed in the first VL images gathered by Metis during the commissioning phase for a total of 60 seconds of exposure time is presented here. A similar analysis is planned for the UV channel. Aims. A prediction of the GCR flux up to hundreds of GeV is made here for the first part of the Solar Orbiter mission to study the Metis coronagraph performance. Methods. GCR model predictions are compared to observations gathered on board Solar Orbiter by the EPD/HET experiment in the range 10 MeV-100 MeV in the summer 2020 and with previous measurements. Estimated cosmic-ray fluxes above 70 MeV n −1 have been also parameterized and used for Monte Carlo simulations aiming at reproducing the cosmic-ray track observations in the Metis coronagraph VL images. 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 cosmicray interactions in the VL detector, it is found that cosmic rays fire a fraction of the order of 10 −4 of the whole image pixel sample. Therefore, cosmic rays do not affect sensibly the quality of Metis VL images. It is also found that the overall efficiency for cosmic-ray identification in the Metis VL images is approximately equal to the contribution of Z>2 particles. As a result, the Metis coronagraph may play the role of a proton monitor for long-term GCR variations during the overall mission duration.