Recent cosmological measurements indicate that baryons comprise about four per cent of the total mass-energy density of the Universe, which is in accord with the predictions arising from studies of the production of the lightest elements. It is also in agreement with the actual number of baryons detected at early times (redshifts z > 2). Close to our own epoch (z < 2), however, the number of baryons detected add up to just over half (approximately 55 per cent) of the number seen at z > 2 (refs 6-11), meaning that about approximately 45 per cent are 'missing'. Here we report a determination of the mass-density of a previously undetected population of baryons, in the warm-hot phase of the intergalactic medium. We show that this mass density is consistent, within the uncertainties, with the mass density of the missing baryons.