Context. High-mass microquasars may produce jets that will strongly interact with surrounding stellar winds on binary system spatial scales. Aims. We study the dynamics of the collision between a mildly relativistic hydrodynamical jet of supersonic nature and the wind of an OB star. Methods. We performed numerical 3D simulations of jets that cross the stellar wind with the code Ratpenat. Results. The jet head generates a strong shock in the wind, and strong recollimation shocks occur due to the initial overpressure of the jet with its environment. These shocks can accelerate particles up to TeV energies and produce gamma-rays. The recollimation shock also strengthens jet asymmetric Kelvin-Helmholtz instabilities produced in the wind/jet contact discontinuity. This can lead to jet disruption even for jet powers of several times 1036 erg s−1. Conclusions. High-mass microquasar jets likely suffer a strong recollimation shock that can be a site of particle acceleration up to very high energies, but also eventually lead to the disruption of the jet.