About ten persistently highly absorbed super-giant high-mass X-ray binaries (sgHMXB) have been discovered by INTEGRAL as bright hard X-ray sources lacking bright X-ray counterparts. Besides IGR J16318-4848, which has peculiar characteristics, the other members of this family share many properties with the classical wind-fed sgHMXB systems. Our goal is to understand the characteristics of highly absorbed sgHMXB and in particular the companion stellar wind, which is thought to be responsible for the strong absorption. We monitored IGR J17252-3616, a highly absorbed system featuring eclipses, with XMM-Newton to study the variability of the column density and the Fe Kα emission line along the orbit and during the eclipses. We also compiled a 3D model of the stellar wind to reproduce the observed variability. We first derive a refined orbital solution based on INTEGRAL, RXTE, and XMM-Newton data. We find that the XMM-Newton monitoring campaign reveals significant variations in the intrinsic absorbing column density along the orbit and the Fe Kα line equivalent width around the eclipse. The origin of the soft X-ray absorption is associated with a dense and extended hydrodynamical tail, trailing the neutron star. This structure extends along most of the orbit, indicating that the stellar wind has been strongly disrupted. The variability of the absorbing column density suggests that the wind velocity is smaller (υ∞≃400km/s) than observed in classical systems. This may also explain the much stronger density perturbation inferred from the observations. Most of the Fe Kα emission is generated in the innermost region of the hydrodynamical tail. This region, which extends over a few accretion radii, is ionized and does not contribute to the soft X-ray absorption. We present a qualitative model of the stellar wind of IGR J17252-3616 that can represent the observations, and we suggest that highly absorbed systems have lower wind velocities than classical sgHMXB. This proposal could be tested with detailed numerical simulations and high-resolution infrared/optical observations. If confirmed, it may turn out that half of the persistent sgHMXB have low stellar wind speeds.