Context. Long-duration gamma-ray bursts (LGRBs) are produced by the collapse of very massive stars. Because of the short life time of their progenitors, LGRBs pinpoint star-forming galaxies. Recent studies demonstrate that LGRBs populate all types of star-forming galaxies from sub-luminous, blue compact dwarfs to luminous infrared galaxies. Aims. We present here a multi-band search for the host galaxy of the long dark GRB 050219A within the enhanced Swift/XRT error circle. We aim to characterise the properties of its host galaxy and compare them with those of other LGRB host galaxies. Methods. We used spectroscopic observations acquired with VLT/X-Shooter to determine the redshift and star-formation rate of the most probable host galaxy identified on the basis of a chance probability criterion. We compared the results with the optical and infrared spectral energy distribution obtained with Swift/UVOT, the seven-channel imager GROND at the 2.2-m telescope on La Silla and the Herschel Space Observatory, supplemented by archival observations obtained with FORS2 at the ESO/VLT, the Spitzer Space Telescope, and the GALEX survey. Results. The most probable host galaxy of the genuine long-duration GRB 050219A is a 3 Gyr-old early-type galaxy at z = 0.211. It is characterised by a ratio of star-formation rate to stellar mass (specific star-formation rate) of ~ 6 × 10-12 yr-1 that is unprecedentedly low when compared to all known LGRB host galaxies. Its properties resemble those of post-starburst galaxies. Conclusions. GRB 050219A might be the first known long burst to explode in a quiescent early-type galaxy. This would be further evidence that GRBs can explode in all kinds of galaxies, with the only requirement being an episode of high-mass star formation.