Context : Aims : We study the Be star \delta Cen circumstellar disk using long-baseline interferometry which is the only observing technique capable of resolving spatially and spectroscopically objects smaller than 5 mas in the H and K band . Methods : We used the VLTI/AMBER instrument on January 6 , 8 , and 9 , 2008 , in the H and K bands to complete low ( 35 ) and medium ( 1500 ) spectral resolution observations . Results : We detected an oscillation in the visibility curve plotted as a function of the spatial frequency which is a clear signature of a companion around \delta Cen . Our best-fit soltution infers a binary separation of 68.7 mas , a companion flux contribution in the K band of about 7 % of the total flux , a PA of 117.5 \degr , and an envelope flux around the Be primary that contributes up to about 50 % of the total flux , in agreement with our Spectral Energy Distribution ( SED ) fit . The envelope size is estimated to be 1.6 mas in K but no departure from spherical symmetry is detected . Conclusions :