Context. The Medium Resolution Spectrometer (MRS) of the Mid-Infrared Instrument (MIRI) on board the James Webb Space Telescope (JWST) will give access to mid-infrared (mid-IR) spectra (5-28 microns) while retaining spatial information. With the unparalleled sensitivity of JWST and the MIRI detectors, the MRS has the potential to revolutionise our understanding of giant exoplanet atmospheres. Aims. Molecular mapping is a promising detection and characterisation technique used to study the spectra of directly imaged exoplanets. We aim to examine the feasibility and application of this technique to MRS observations. Methods. We used the instrument simulator MIRISIM to create mock observations of resolved star and exoplanet systems. As an input for the simulator, we used stellar and planet parameters from literature, with the planet spectrum being modelled with the radiative transfer code petitRADTRANS. After processing the raw data with the JWST pipeline, we high pass filter the data to account for the stellar point spread function (PSF), and used a forward modelling approach to detect the companions and constrain the chemical composition of their atmospheres through their molecular signatures. Results. We identified limiting factors in spectroscopic characterisation of directly imaged exoplanets with the MRS and simulated observations of two representative systems, HR8799 and GJ504. In both systems, we could detect the presence of multiple molecules that were present in the input model of their atmospheres. We used two different approaches with single molecule forward models, used in literature, that are sensitive to detecting mainly H 2 O, CO, CH 4 , and NH 3 , and a log-likelihood ratio test that uses full atmosphere forward models and is sensitive to a larger number of less dominant molecular species. Conclusions. We show that the MIRI MRS can be used to characterise widely separated giant exoplanets in the mid-IR using molecular mapping. Such observations would provide invaluable information for the chemical composition of the atmosphere, complementing other JWST observing modes, as well as ground-based observations.