AGN feedback now appears as an attractive mechanism to resolve some of the outstanding problems with the "standard" cosmological models, in particular those related to massive galaxies. At low redshift, evidence is growing that gas cooling and star formation may be efficiently suppressed by mechanical energy input from radio sources. To directly constrain how this may influence the formation of massive galaxies near the peak in the redshift distribution of powerful quasars, z ∼ 2, we present an analysis of the emission-line kinematics of 3 powerful radio galaxies at z ∼ 2−3 (HzRGs) based on rest-frame optical integral-field spectroscopy obtained with SINFONI on the VLT. The host galaxies of powerful radio-loud AGN are among the most massive galaxies, and thus AGN feedback may have a particularly clear signature in these galaxies. We find evidence for bipolar outflows in all HzRGs, with kinetic energies that are equivalent to 0.2% of the rest-mass of the supermassive black hole. Observed total velocity offsets in the outflows are ∼800−1000 km s −1 between the blueshifted and redshifted line emission, and FWHMs ∼ 1000 km s −1 suggest strong turbulence. Line ratios allow to measure electron temperatures, ∼10 4 K from [OIII]λλλ4363, 4959, 5007 at z ∼ 2, electron densities (∼500 cm −3 ) and extinction (A V ∼ 1−4 mag). Ionized gas masses estimated from the Hα luminosity are of order 10 10 M , similar to the molecular gas content of HzRGs, underlining that these outflows may indicate a significant phase in the evolution of the host galaxy. The total energy release of ∼10 60 erg during a dynamical time of ∼10 7 yrs corresponds to about the binding energy of a massive galaxy, similar to the prescriptions adopted in galaxy evolution models. Geometry, timescales and energy injection rates of order 10% of the kinetic energy flux of the jet suggest that the outflows are most likely driven by the radio source. The global energy density release of ∼10 57 erg s −1 Mpc −3 may also influence the subsequent evolution of the HzRG by enhancing the entropy and pressure in the surrounding halo and facilitating ram-pressure stripping of gas in satellite galaxies that may contribute to the subsequent mass assembly of the HzRG through low-dissipation "dry" mergers.