Context. The Sloan Digital Sky Survey (SDSS) and Wide-field Infrared Survey Explorer (WISE) provide information about the surface composition of about 100 000 minor planets. The resulting visible colors and albedos enabled us to group them in several major classes, which are a simplified view of the diversity shown by the few existing spectra. A large set of data in the 0.8-2.5 μm, where wide spectral features are expected, is required to refine and complement the global picture of these small bodies of the solar system. Aims: We aim to obtain the near-infrared colors for a large sample of solar system objects using the observations made during the VISTA-VHS survey. Methods: We performed a serendipitous search in VISTA-VHS observations using a pipeline developed to retrieve and process the data that corresponds to solar system objects (SSo). The resulting photometric data is analyzed using color-color plots and by comparison with the known spectral properties of asteroids. Results: The colors and the magnitudes of the minor planets observed by the VISTA survey are compiled into three catalogs that are available online: the detections catalog (MOVIS-D), the magnitudes catalog (MOVIS-M), and the colors catalog (MOVIS-C). They were built using the third data release of the survey (VISTA VHS-DR3). A total of 39 947 objects were detected, including 52 NEAs, 325 Mars Crossers, 515 Hungaria asteroids, 38 428 main-belt asteroids, 146 Cybele asteroids, 147 Hilda asteroids, 270 Trojans, 13 comets, 12 Kuiper Belt objects and Neptune with its four satellites. The colors found for asteroids with known spectral properties reveal well-defined patterns corresponding to different mineralogies. The distributions of MOVIS-C data in color-color plots shows clusters identified with different taxonomic types. All the diagrams that use (Y - J) color separate the spectral classes more effectively than the (J - H) and (H - Ks) plots used until now: even for large color errors (<0.1), the plots (Y - J) vs. (Y - Ks) and (Y - J) vs. (J - Ks) provide the separation between S-complex and C-complex. The end members A, D, R, and V-types occupy well-defined regions. The catalogs are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/591/A115