Context : The Be stars are massive dwarf or subgiant stars that present temporary emission lines in their spectrum , and particularly in the H { \alpha } line . The mechanism triggering these Be episodes is currently unknown , but binarity could play an important role . Aims : Previous observations with the VLT/VISIR instrument ( Kervella & Domiciano de SouzaƂ 2007 ) revealed a faint companion to Achernar , the brightest Be star in the sky . The present observations are intended to characterize the physical nature of this object . Methods : We obtained near-IR images and an H-band spectrum of Achernar B using the VLT/NACO adaptive optics systems . Results : Our images clearly show the displacement of Achernar B over a portion of its orbit around Achernar A . Although there are not enough data to derive the orbital parameters , they indicate a period of about 15 yr . The projected angular separation of the two objects in December 2007 was less than 0.15 \arcsec , or 6.7 AU at the distance of Achernar . Conclusions : From its flux distribution in the near- and thermal-infared , Achernar B is most likely an A1V-A3V star . Its orbital period appears similar to the observed pseudo-periodicity of the Be phenomenon of Achernar . This indicates that an interaction between A and B at periastron could be the trigger of the Be episodes .