Context. The detectors of the JWST Mid-Infrared Instrument (MIRI) Medium Resolution Spectrometer (MRS) form low-finesse resonating cavities that cause periodic count rate modulations (fringes) with peak amplitudes of up to 15% for sources external to MIRI. To detect weak features on a strong continuum and reliably measure line fluxes and line-flux ratios, fringe correction is crucial. Aims. This paper describes the first of two steps implemented in the JWST Science Calibration Pipeline, which is the division by a static fringe flat that removes the bulk of the fringes for extended sources. Methods. Fringe flats were derived by fitting a numerical model to observations of spatially extended sources. The model includes fringes that originate from two resonating cavities in the detector substrate (a third fringe component that originates from the dichroic filters is not included). The model, numerical implementation, and resulting fringe flats are described, and the efficiency of the calibration was evaluated for sources of various spatial extents on the detector. Results. Flight fringe flats are obtained from observations of the planetary nebula NGC 7027. The two fringe components are well recovered and fitted by the model. The derived parameters are used to build a fringe flat for each MRS spectral band, except for 1A and 1B due to the low signal-to-noise ratio of NGC 7027 in these bands. When applied to extended sources, fringe amplitudes are reduced to the sub-percent level on individual spaxels. For point sources, they are reduced to amplitudes between 1 and 5% considering individual spaxels and a single dither position, and decrease to the 1 to 2% level after two-dimensional residual fringe correction. Conclusions. The fringe flats derived from this work are the reference files currently in use by the JWST Science Calibration Pipeline. They provide an efficient calibration for extended sources, and are less efficient for point sources. Future improvements of these fringe flats are possible. The fringe modelling method could also be tested on individual semi-extended or point sources.