Context. Vela X-1, a prototypical high-mass X-ray binary (HMXB), hosts a neutron star (NS) in a close orbit around an early-B supergiant donor star. Accretion of the donor star's wind onto the NS powers its strong X-ray luminosity. To understand the physics of HMXBs, detailed knowledge about the donor star winds is required. Aims. To gain a realistic picture of the donor star in Vela X-1, we constructed a hydrodynamically consistent atmosphere model describing the wind stratification while properly reproducing the observed donor spectrum. To investigate how X-ray illumination affects the stellar wind, we calculated additional models for different X-ray luminosity regimes. Methods. We used the recently updated version of the Potsdam Wolf–Rayet code to consistently solve the hydrodynamic equation together with the statistical equations and the radiative transfer. Results. The wind flow in Vela X-1 is driven by ions from various elements, with Fe iii and S iii leading in the outer wind. The model-predicted mass-loss rate is in line with earlier empirical studies. The mass-loss rate is almost unaffected by the presence of the accreting NS in the wind. The terminal wind velocity is confirmed at v_∞≈ 600 km s⁻¹. On the other hand, the wind velocity in the inner region where the NS is located is only ≈100 km s⁻¹, which is not expected on the basis of a standard β-velocity law. In models with an enhanced level of X-rays, the velocity field in the outer wind can be altered. If the X-ray flux is too high, the acceleration breaks down because the ionization increases. Conclusions. Accounting for radiation hydrodynamics, our Vela X-1 donor atmosphere model reveals a low wind speed at the NS location, and it provides quantitative information on wind driving in this important HMXB.