Massive stars provide feedback that shapes the interstellar medium of galaxies at all redshifts and their resulting stellar populations. Here we present three adaptive mesh refinement radiation hydrodynamics simulations that illustrate the impact of momentum transfer from ionizing radiation to the absorbing gas on star formation in high-redshift dwarf galaxies. Momentum transfer is calculated by solving the radiative transfer equation with a ray-tracing algorithm that is adaptive in spatial and angular coordinates. We find that momentum input partially affects star formation by increasing the turbulent support to a three-dimensional rms velocity equal to the circular velocity of early haloes. Compared to a calculation that neglects radiation pressure, the star formation rate is decreased by a factor of 5 to 1.8 × 10−2 M⊙ yr−1 in a dwarf galaxy with a dark matter and stellar mass of 2.0 × 108 and 4.5 × 105 M⊙, respectively, when radiation pressure is included. Its mean metallicity of 10−2.1 Z⊙ is consistent with the observed dwarf galaxy luminosity–metallicity relation. However, one may naively expect from the calculation without radiation pressure that the central region of the galaxy overcools and produces a compact, metal-rich stellar population with an average metallicity of 0.3 Z⊙, indicative of an incorrect physical recipe. In addition to photoheating in H ii regions, radiation pressure further drives dense gas from star-forming regions, so supernova feedback occurs in a warmer and more diffuse medium, launching metal-rich outflows. Capturing this aspect and a temporal separation between the start of radiative and supernova feedback are numerically important in the modelling of galaxies to avoid the ‘overcooling problem’. We estimate that dust in early low-mass galaxies is unlikely to aid in momentum transfer from radiation to the gas.