The "Neutrino Experiment with a Xenon Time-Projection Chamber" (NEXT) experiment intends to investigate the neutrinoless double beta decay of 136Xe, and therefore requires a severe suppression of potential backgrounds. An extensive material screening and selection process was undertaken to quantify the radioactivity of the materials used in the experiment. Separate energy and tracking readout planes using different sensors allow us to combine the measurement of the topological signature of the event for background discrimination with the energy resolution optimization. The design of radiopure readout planes, in direct contact with the gas detector medium, was especially challenging since the required components typically have activities too large for experiments demanding ultra-low background conditions. After studying the tracking plane, here the radiopurity control of the energy plane is presented, mainly based on gamma-ray spectroscopy using ultra-low background germanium detectors at the Laboratorio Subterr&aposaneo de Canfranc (Spain). All the available units of the selected model of photomultiplier have been screened together with most of the components for the bases, enclosures and windows. According to these results for the activity of the relevant radioisotopes, the selected components of the energy plane would give a contribution to the overall background level in the region of interest of at most 2.4×10-4 counts keV-1 kg-1 y-1, satisfying the sensitivity requirements of the NEXT experiment.