The discovery of multiple stellar populations (multiple in the sense of inhomogeneous chemical abundances, with specific patterns of variations of a few light elements) in Galactic globular clusters and massive intermediate-age and old clusters in the Magellanic Clouds, both through spectroscopy and photometry, has led to a major change in our views about the formation of these objects. To date, none of the proposed scenarios are able to quantitatively explain all the chemical patterns observed in individual clusters. An extension of the study of multiple populations to resolved extragalactic massive clusters beyond the Magellanic Clouds would therefore be welcome, as it would enable the investigation and characterisation of the presence of multiple populations in different environments and age ranges. To this purpose, the James Webb Space Telescope (JWST) can potentially play a major role. On the one hand, the JWST promises direct observations of proto-globular cluster candidates at high redshift, and on the other hand, it can potentially push the sample of resolved clusters with detected multiple populations to larger distances. In this paper we address this second goal. Using theoretical stellar spectra and stellar evolution models, we investigated the effect of multiple population chemical patterns on synthetic magnitudes in the JWST infrared NIRCam filters. We identified the colours (F150W − F460M), (F115W − F460M) and pseudocolours C_{F150W, F460M, F115W} = (F150W − F460M)−(F460M − F115W), C_{F150W, F277W, F115W} = (F150W − F277W)−(F277W − F115W), as diagnostics able to reveal the presence of multiple populations along the red giant branches of old and intermediate-age clusters. Using the available online simulator for the NIRCam detector, we estimated that multiple populations can be potentially detected – depending on the exposure times, exact filter combination used, and extent of the abundance variations and the cluster [Fe/H] – out to a distance of ∼5 Mpc (approximately the distance to the M83 group).