ABSTRACT We investigate extremely red quasars (ERQs), a remarkable population of heavily reddened quasars at redshift z ∼ 2−3 that might be caught during a short-lived ‘blow-out’ phase of quasar/galaxy evolution. We perform a near-IR observational campaign using Keck/NIRSPEC, VLT/X-shooter, and Gemini/GNIRS to measure rest-frame optical spectra of 28 ERQs with median infrared luminosity 〈log L(erg s−1)〉 ∼ 46.2. They exhibit the broadest and most blueshifted [O iii] λ4959,5007 emission lines ever reported, with widths (w90) ranging between 2053 and 7227 km s−1, and maximum outflow speeds (v98) up to 6702 km s−1. ERQs on average have [O iii] outflows velocities about three times larger than those of luminosity-matched blue quasar samples. This discrepancy can be explained by a strong correlation between [O iii] kinematics and i–W3 colour, and not by radio loudness, or higher Eddington ratios. We estimate for these objects that at least 3–5 per cent of their bolometric luminosity is being converted into the kinetic power of the observed wind. Our results reveal that ERQs have the potential to strongly affect the evolution of host galaxies.