In this paper, we examine in detail the key structural properties of high‐redshift dark matter haloes as a function of their spin parameter. We perform and analyse high‐resolution cosmological simulations of the formation of structure in a Λ cold dark matter universe. We study the mass function, shapes, density profiles and rotation curves for a large sample of dark matter haloes from z= 15 to 6. We also present detailed convergence tests for individual haloes. We find that high‐spin haloes have stronger clustering strengths (up to 25 per cent) at all mass and redshift ranges at these early epochs. High‐redshift spherical haloes are also up to 50 per cent more clustered than extremely aspherical haloes. High‐spin haloes at these redshifts are also preferentially found in high‐density environments, and have more neighbours than their low‐spin counterparts. We report a systematic offset in the peak of the circular velocity curves for high‐ and low‐spin haloes of the same mass. Therefore, estimating halo masses without knowledge of the spin, using only the circular velocity can yield errors of up to 40 per cent. The significant dependence of key structural properties on spin that we report here likely has important implications for studies of star formation and feedback from these galaxies.