Context. The newly accessible mid-infrared (MIR) window offered by the James Webb Space Telescope (JWST) for exoplanet imaging is expected to provide valuable information to characterize their atmospheres. In particular, coronagraphs on board the JWST Mid-InfraRed instrument (MIRI) are capable of imaging the coldest directly imaged giant planets at the wavelengths where they emit most of their flux. The MIRI coronagraphs have been specially designed to detect the NH3 absorption around 10.5 μm, which has been predicted by atmospheric models and should be detectable for planets colder than 1200 K. Aims. We aim to assess the presence of NH3 while refining the atmospheric parameters of one of the coldest companions detected by directly imaging GJ 504 b. Its mass is still a matter of debate and depending on the host star age estimate, the companion could either be placed in the brown dwarf regime of ~20 MJup or in the young Jovian planet regime of ~4 MJup. Methods. We present an analysis of new MIRI observations, using the coronagraphic filters F1065C, F1140C, and F1550C of the GJ 504 system. We took advantage of previous observations of reference stars to build a library of images and to perform a more efficient subtraction of the stellar diffraction pattern. We used an atmospheric grid from the Exo-REM model to refine the atmospheric parameters by combining archival near-infrared (NIR) photometry with the MIR photometry. Results. We detected the presence of NH3 at 12.5 σ and measured its volume mixing ratio of 10- 5.3±0.07 in the atmosphere of GJ 504 b. These results are in line with atmospheric model expectations for a planetary-mass object and observed in brown dwarfs within a similar temperature range. The best-fit model with Exo-REM provides updated values of its atmospheric parameters, yielding a temperature of Teff = 512 ± 10 K and radius of R = 1.08- 0.03+0.04 RJup. Conclusions. These observations demonstrate the capability of MIRI coronagraphs to detect NH3 and to provide the first MIR observations of one of the coldest directly imaged companions. Overall, NH3 is a key molecule for characterizing the atmospheres of cold planets, offering valuable insights into their surface gravity. These observations provide valuable information for future spectroscopic observations planned with JWST, in particular, with the MIRI medium-resolution spectrometer (MRS), which will allow us to characterize the atmosphere of GJ 504 b in depth.