The evolution of a linearly polarized, long-wavelength Alfvén wave propagating in a collisionless magnetized plasma with a sheared parallel-directed velocity flow is here studied by means of two-dimensional hybrid Vlasov–Maxwell (HVM) simulations. The unperturbed sheared flow has been represented by an exact solution of the HVM set of equations of (Malara et al., Phys. Rev. E, vol. 97, 2018, 053212), thus avoiding spurious oscillations that would arise from the non-stationary initial state and inevitably affect the dynamics of the system. We have considered the evolution of both a small and a moderate amplitude Alfvén wave, in order to separate linear wave–shear flow couplings from kinetic effects, the latter being more relevant for larger wave amplitudes. The phase mixing generated by the shear flow modifies the initial perturbation, leading to the formation of small-scale transverse fluctuations at scales comparable with the proton inertial length/Larmor radius. By analysing both the polarization and group velocity of perturbations in the shear regions, we identify them as kinetic Alfvén waves (KAWs). In the moderate amplitude run, kinetic effects distort the proton distribution function in the shear region. This leads to the formation of a proton beam, at the Alfvén speed and parallel to the magnetic field. Such a feature, due to the parallel electric field associated with KAWs, positively compares with solar wind observations of suprathermal ion populations, suggesting that it may be related to the presence of ion-scale KAW-like fluctuations.