Future astrophysical surveys such as J-PAS will produce very large datasets, the so-called "big data", which will require the deployment of accurate and efficient machine-learning (ML) methods. In this work, we analyze the miniJPAS survey, which observed about ~1deg^2^ of the AEGIS field with 56 narrow-band filters and 4 ugri broad-band filters. The miniJPAS primary catalog contains approximately 64 000 objects in the r detection band (mag_AB_<~24), with forced-photometry in all other filters. We discuss the classification of miniJPAS sources into extended (galaxies) and point-like (e.g., stars) objects, which is a step required for the subsequent scientific analyses. We aim at developing an ML classifier that is complementary to traditional tools that are based on explicit modeling. In particular, our goal is to release a value-added catalog with our best classification. In order to train and test our classifiers, we cross-matched the miniJPAS dataset with SDSS and HSC-SSP data, whose classification is trustworthy within the intervals 15<=r<=20 and 18.5<=r<=23.5, respectively. We trained and tested six different ML algorithms on the two cross-matched catalogs: K-nearest neighbors, decision trees, random forest (RF), artificial neural networks, extremely randomized trees (ERT), and an ensemble classifier. This last is a hybrid algorithm that combines artificial neural networks and RF with the J-PAS stellar and galactic loci classifier. As input for the ML algorithms we used the magnitudes from the 60 filters together with their errors, with and without the morphological parameters. We also used the mean point spread function in the r detection band for each pointing. We find that the RF and ERT algorithms perform best in all scenarios. When the full magnitude range of 15<=r~21). We use our best classifiers, with and without morphology, in order to produce a value-added catalog.