HD~106906AB is so far the only young binary system around which a planet has been imaged and a debris disk evidenced thanks to a strong IR excess. As such, it represents a unique opportunity to study the dynamics of young planetary systems. We aim at further investigating the close (tens of au scales) environment of the HD~106906AB system. We used the extreme AO fed, high contrast imager SPHERE recently installed on the VLT to observe HD~106906. Both the IRDIS imager and the Integral Field Spectrometer were used. We discovered a very inclined, ring-like disk at a distance of 65~au from the star. The disk shows a strong brightness asymmetry with respect to its semi-major axis. It shows a smooth outer edge, compatible with ejection of small grains by the stellar radiation pressure. We show furthermore that the planets projected position is significantly above the disks PA. Given the determined disk inclination, it is not excluded though that the planet could still orbit within the disk plane if at a large separation (2000--3000 au). We identified several additional point sources in the SPHERE/IRDIS field-of-view, that appear to be background objects. We compare this system with other debris disks sharing similarities, and we briefly discuss the present results in the framework of dynamical evolution.
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