Giant radio haloes in galaxy clusters are the primary evidence for the existence of relativistic particles (cosmic rays) and magnetic fields over Mpc scales. Observational tests for the different theoretical models explaining their powering mechanism have so far been obtained through X-ray selection of clusters, e.g. by comparing cluster X-ray luminosities with radio halo power. Here we present the first global scaling relations between radio halo power and integrated Sunyaev–Zel’dovich (SZ) effect measurements, using the Planck all-sky cluster catalogue and published radio data. The correlation agrees well with previous scaling measurements based on X-ray data and offers a more direct probe into the mass dependence inside radio haloes. However, we find no strong indication for a bi-modal cluster population split between radio halo and radio-quiet objects. We discuss the possible causes for this apparent lack of bi-modality and compare the observed slope of the radio–SZ correlation with competing theoretical models of radio halo origin.