Primordial stars are key to primeval structure formation as the first stellar components of primeval galaxies, the sources of cosmic chemical enrichment and likely cosmic reionization, and they possibly gave rise to the super-massive black holes residing at the centres of galaxies today. While the direct detection of individual Pop III stars will likely remain beyond reach for decades to come, we show their supernova remnants may soon be detectable in the radio. We calculate radio synchrotron signatures between 0.5 and 35 GHz from hydrodynamical computations of the supernova remnants of Pop III stars in ∼107 M⊙ minihaloes. We find that hypernovae yield the brightest systems, with observed radio fluxes as high as 1–10 μJy. Less energetic Type II supernovae yield remnants about a factor of 30 dimmer and pair-instability supernova remnants are dimmer by a factor of more than 10 000. Because of the high gas densities of the progenitor environments, synchrotron losses severely limit the maximum emission frequencies, producing a distinctive peaked radio spectrum distinguishable from normal galactic supernova remnant spectra. Hypernovae radio remnants should be detectable by existing radio facilities like eVLA and eMERLIN while Type II supernova remnants will require the Square Kilometre Array. The number counts of hypernova remnants at z > 20 with fluxes above 1 μJy are expected to be one per hundred square degree field, increasing to a few per square degree if they form down to z = 10. The detection of a z > 20 Type II supernova remnant brighter than 1 nJy would require a 100–200 deg2 field, although only a 1–2 deg2 field for those forming down to z = 10. Hypernova and Type II supernova remnants are easily separated from one another by their light curves, which will enable future surveys to use them to constrain the initial mass function of Pop III stars.