The Mid-Infrared instrument ( MIRI ) on board the James Webb Space Telescope will perform the first ever characterization of young giant exoplanets observed by direct imaging in the 5-28 \mu m spectral range . This wavelength range is key for both determining the bolometric luminosity of the cool known exoplanets and for accessing the strongest ammonia bands . In conjunction with shorter wavelength observations , MIRI will enable a more accurate characterization of the exoplanetary atmospheric properties . Here we consider a subsample of the currently known exoplanets detected by direct imaging and we discuss their detectability with MIRI , either using the coronagraphic or the spectroscopic modes . By using the Exo-REM atmosphere model we calculate the mid-infrared emission spectra of fourteen exoplanets , and we simulate MIRI coronagraphic or spectroscopic observations . Specifically we analyze four coronagraphic observational setups , which depend on ( i ) the target-star and reference-star offset ( 0 , 3 , 14 mas ) , ( ii ) the wave-front-error ( 130 , 204 nm rms ) , ( iii ) the telescope jitter amplitude ( 1.6 , 7 mas ) . We then determine the signal-to-noise and integration time values for the coronagraphic targets whose planet-to-star contrasts range from 3.9 to 10.1 mag . We conclude that all the MIRI targets should be observable with different degrees of difficulty , which depends on the final in-flight instrument performances . Furthermore , we test for detection of ammonia in the atmosphere of the coolest targets . Finally , we present the case of HR 8799 b to discuss what MIRI observations can bring to the knowledge of a planetary atmosphere , either alone or in combination with shorter wavelength observations .