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 b and. 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 (150 0) spectral resolution observations. We detected an oscillation in the visibility curve plotted as a function of the spatial frequency which is a clear signat ure of a companion around $delta$ Cen. Our best-fit soltution infers a binary separation of 68.7 mas, a companion flux co ntribution 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 e nvelope size is estimated to be 1.6 mas in K but no departure from spherical symmetry is detected.