Context. X-ray observations have unveiled the existence of enigmatic point-like sources at the center of young (a few kyrs) supernova remnants. These sources, known as central compact objects (CCOs), are thought to be neutron stars produced by the supernova explosion, although their X-ray phenomenology makes them markedly different from all other young neutron stars discovered to date. Aims. The aim of this work is to search for the optical/IR counterpart of the Vela Junior CCO and to understand the nature of the associated Ha nebula discovered by Pellizzoni et al. ( 2002). Methods. We used deep optical ( R-band) and IR (J, H, K-s-bands) observations recently performed by our group with the ESO VLT to obtain the first deep, high resolution images of the field to resolve the nebula structure and pinpoint a point-like source possibly associated with the neutron star. Results. Our R-band image shows that the nebula's flux and structure are very similar to those of, the Ha one, suggesting that the nebula spectrum is dominated by pure Ha line emission. However, the nebula is not detected in our IR observations, which makes it impossible to to constrain its spectrum. A faint point-like object ( J >= 22.6, H similar to 21.6, Ks similar to 21.4) compatible with the neutron star's Chandra X-ray position is detected in our IR images (H and K-s) but not in the optical image ( R greater than or similar to 25.6), where it is buried by the nebula background. Conclusions. The nebula is most likely a bow-shock produced by the neutron star motion through the ISM or, alternatively, a photoionization nebula powered by UV radiation from a hot neutron star. A synchrotron nebula, powered by the relativistic particle wind from the neutron star, is the less likely interpretation because of its non-detection in the X-rays and the apparent lack of continuum emission. The candidate CCO counterpart could be the neutron star itself, a fallback disk left over from the supernova explosion, or a mid M-type star, or later, at a distance of 2 kpc.