Context. The International Gamma-Ray Astrophyiscs Laboratory (INTEGRAL) is discovering a large number of new hard X-ray sources, many of them being HMXBs. The identification and spectral characterization of their optical/infrared counterparts is a necessary step to undertake detailed study of these systems. In particular, the determination of the spectral type is crucial in the case of the new class of Supergiant Fast X-ray Transients (SFXTs), which show X-ray properties common to other objects. Aims. Our goal is to perform spectral analysis and classification of proposed counterparts to HMXBs in order to characterize the system they belong to. Methods. We used the ESO/NTT SofI spectrograph to observe proposed IR counterparts to HMXBs, obtaining Ks medium resolution spectra (R = 1320) with a S/N 􏰀 100. We classified them through comparison with published atlases. Results. We were able to spectrally classify the six sources. This allowed us to ascribe one of them to the new class of SFXTs and confirm the membership of two sources to this class. We confirmed the spectral classification, derived from optical spectroscopy, of a known system, 4U 1907-09, showing for the first time its infrared spectrum. The spectral classification was also used to estimate the distance of the sources. We compared the extinction as derived from X-ray data with effective interstellar extinction obtained from our data, discussing the absorption component due to the circumstellar environment, which we observed in four systems; in particular, intrinsic absorption seems to emerge as a typical feature of the entire class of SFXTs.