We report the discovery of a bright, brown dwarf companion to the star HIP 64892, imaged with VLT/SPHERE during the SHINE exoplanet survey. The host is a B9.5V member of the Lower-Centaurus-Crux subgroup of the Scorpius Centaurus OB association. The measured angular separation of the companion (1.2705 +/- 0.0023) corresponds to a projected distance of 159 +/- 12AU. We observed the target with the dual-band imaging and long-slit spectroscopy modes of the IRDIS imager to obtain its spectral energy distribution (SED) and astrometry. In addition, we reprocessed archival NACO L-band data, from which we also recover the companion. Its SED is consistent with a young (<30 Myr), low surface gravity object with a spectral type of M9 gamma +/- 1. From comparison with the BT-Settl atmospheric models we estimate an effective temperature of T-eff = 2600 +/- 100 K, and comparison of the companion photometry to the COND evolutionary models yields a mass of similar to 29-37 M-J at the estimated age of 16(-7)(+15) Myr for the system. The star HIP 64892 is a rare example of an extreme-mass ratio system (q similar to 0.01) and will be useful for testing models relating to the formation and evolution of such low-mass objects.