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Future astrophysical surveys such as J-PAS will produce very large datasets, which will require the deployment of accurate and efficient Machine Learning (ML) methods. In this work, we analyze the miniJPAS survey, which observed about 1 deg2 of the AEGIS field with 56 narrow-band filters and 4 ugri broad-band filters. We discuss the classification of miniJPAS sources into extended (galaxies) and point-like (e.g. stars) objects, a necessary step for the subsequent scientific analyses. We aim at developing an ML classifier that is complementary to traditional tools based on explicit modeling. In order to train and test our classifiers, we crossmatched the miniJPAS dataset with SDSS and HSC-SSP data. We trained and tested 6 different ML algorithms on the two crossmatched catalogs. As input for the ML algorithms we use the magnitudes from the 60 filters together with their errors, with and without the morphological parameters. We also use the mean PSF in the r detection band for each pointing. We find that the RF and ERT algorithms perform best in all scenarios. When analyzing the full magnitude range of 15<r<23.5 we find AUC=0.957 with RF when using only photometric information, and AUC=0.986 with ERT when using photometric and morphological information. Regarding feature importance, when using morphological parameters, FWHM is the most important feature. When using photometric information only, we observe that broad bands are not necessarily more important than narrow bands, and errors are as important as the measurements. ML algorithms can compete with traditional star/galaxy classifiers, outperforming the latter at fainter magnitudes (r>21). We use our best classifiers, with and without morphology, in order to produce a value added catalog available at https://j-pas.org/datareleases .