Context. The INTEGRAL mission has led to the discovery of a new type of supergiant X-ray binaries (SGXBs), whose physical properties differ from those of previously known SGXBs. Those sources are in the course of being unveiled by means of multi-wavelength X-rays, optical, near- and mid-infrared observations, and two classes are appearing. The first class consists of obscured persistent SGXBs and the second is populated by the so-called supergiant fast X-ray transients (SFXTs). Aims. We report here mid-infrared (MIR) observations of the companion stars of twelve SGXBs from these two classes in order to assess the contribution of the star and the material enshrouding the system to the total emission. Methods. We used data from observations we carried out at ESO/VLT with VISIR, as well as archival and published data, to perform broad-band spectral energy distributions of the companion stars and fitted them with a combination of two black bodies representing the star and a MIR excess due to the absorbing material enshrouding the star, if there was any. Results. We detect a MIR excess in the emission of IGR J16318- 4848, IGR J16358-4726, and perhaps IGR J16195-4945. The other sources do not exhibit any MIR excess even when the intrinsic absorption is very high. Indeed, the stellar winds of supergiant stars are not suitable for dust production, and we show that this behaviour is not changed by the presence of the compact object. Concerning IGR J16318-4848 and probably IGR J16358-4726, the MIR excess can be explained by their sgBe nature and the presence of an equatorial disk around the supergiant companion in which dust can be produced. Moreover, our results suggest that some of the supergiant stars in those systems could exhibit an absorption excess compared to isolated supergiant stars, this excess being possibly partly due to the photoionisation of their stellar wind in the vicinity of their atmosphere. We also show that the differences in behaviour between the obscured SGXBs and the SFXTs in the high-energy domain do not exist from optical-to-MIR wavelength. Supergiant stars in SFXTs could nevertheless be most of the time less absorbed than supergiant stars in obscured SGXBs, due to the geometry of the systems. At last, our results confirm a very dense cocoon of material around the compact object as the extinction in the X-ray domain is generally several orders of magnitude higher than the extinction in the visible.