The Galactic Centre hosts a puzzling stellar population in its inner few parsecs, with a high abundance of surprisingly young, relatively massive stars bound within the deep potential well of the central supermassive black hole, Sagittarius A* (ref. 1). Previous studies suggest that the population of objects emitting soft X-rays (less than 10 kiloelectronvolts) within the surrounding hundreds of parsecs, as well as the population responsible for unresolved X-ray emission extending along the Galactic plane, is dominated by accreting white dwarf systems. Observations of diffuse hard-X-ray (more than 10 kiloelectronvolts) emission in the inner 10 parsecs, however, have been hampered by the limited spatial resolution of previous instruments. Here we report the presence of a distinct hard-X-ray component within the central 4 × 8 parsecs, as revealed by subarcminute-resolution images in the 20-40 kiloelectronvolt range. This emission is more sharply peaked towards the Galactic Centre than is the surface brightness of the soft-X-ray population. This could indicate a significantly more massive population of accreting white dwarfs, large populations of low-mass X-ray binaries or millisecond pulsars, or particle outflows interacting with the surrounding radiation field, dense molecular material or magnetic fields. However, all these interpretations pose significant challenges to our understanding of stellar evolution, binary formation, and cosmic-ray production in the Galactic Centre.