We present the unplanned detection of a white dwarf companion to the star HD 218261 in mid-infrared (10-16 μm) observations with JWST/MIRI. This star was observed as a calibrator for coronagraphic observations of the exoplanet host HR 8799. HD 218261 B has only previously been detected by Gaia, and only in visible light. We confidently detect the companion in the mid-infrared, where it is less luminous than the primary by a factor of ∼104. The visible and mid-infrared photometry are consistent with a white dwarf of Teff ≈ 10000 K, M ≈ 0.8 M⊙, though observation of its optical spectrum is required to precisely constrain its physical parameters. These results demonstrate that precise mid-infrared photometry of white dwarf companions to bright stars can be obtained with MIRI, opening up new possibilities for studying white dwarfs in close binaries.