Context. Young giant planets are the best targets for characterization with direct imaging. The Medium Resolution Spectrometer (MRS) of the Mid-Infrared Instrument (MIRI) of the recently launched James Webb Space Telescope (JWST) will give access to the first spectroscopic data for direct imaging above 5 µm with unprecedented sensitivity at a spectral resolution of up to 3700. This will provide a valuable complement to near-infrared data from ground-based instruments for characterizing these objects. Aims. We aim to evaluate the performance of MIRI/MRS in detecting molecules in the atmosphere of exoplanets and in constraining atmospheric parameters using Exo-REM atmospheric models. Methods. The molecular mapping technique based on cross-correlation with synthetic models was recently introduced. We test this promising detection and characterization method on simulated MIRI/MRS data. Results. Directly imaged planets can be detected with MIRI/MRS, and we are able to detect molecules (H 2 O, CO, NH 3 , CH 4 , HCN, PH 3 , CO 2 ) at various angular separations depending on the strength of the molecular features and brightness of the target. We find that the stellar spectral type has a weak impact on the detection level. This method is globally most efficient for planets with temperatures below 1500 K, for bright targets, and for angular separations of greater than 1′′. Our parametric study allows us to anticipate the ability to characterize planets that will be detected in the future. Conclusions. The MIRI/MRS will give access to molecular species not yet detected in exoplanetary atmospheres. The detection of molecules acting as indicators of the temperature of the planets will make it possible to discriminate between various hypotheses of the preceding studies, and the derived molecular abundance ratios should bring new constraints on planet-formation scenarios.