We present a supervised machine learning methodology to classify stellar populations in the Local Group dwarf-irregular galaxy NGC 6822. Near-IR colours (J-H, H-K, and J-K), K-band magnitudes and far-IR surface brightness (at 70 and 160um) measured from Spitzer and Herschel images are the features used to train a Probabilistic Random Forest (PRF) classifier. Point-sources are classified into eight target classes: young stellar objects (YSOs), oxygen- and carbon-rich asymptotic giant branch stars, red giant branch and red supergiant stars, active galactic nuclei, massive main-sequence stars, and Galactic foreground stars. The PRF identifies sources with an accuracy of ~90 per cent across all target classes rising to ~96 per cent for YSOs. We confirm the nature of 125 out of 277 literature YSO candidates with sufficient feature information, and identify 199 new YSOs and candidates. Whilst these are mostly located in known star-forming regions, we have also identified new star formation sites. These YSOs have mass estimates between ~15 and 50M_{sun}_, representing the most massive YSO population in NGC 6822. Another 82 out of 277 literature candidates are definitively classified as non-YSOs by the PRF analysis. We characterize the star formation environment by comparing the spatial distribution of YSOs to those of gas and dust using archival images. We also explore the potential of using (unsupervised) t-distributed stochastic neighbour embedding maps for the identification of the same stellar population classified by the PRF.