Context. The MOVIS catalog contains the largest set of near-infrared (NIR) colors for solar system objects. These data were obtained from the observations performed by VISTA-VHS survey using the Y, J, H, and Ks filters. The taxonomic classification of objects in this catalog allows us to obtain large-scale distributions for the asteroidal population, to study faint objects, and to select targets for detailed spectral investigations. Aims: We aim to provide a taxonomic classification for asteroids observed by VISTA-VHS survey. We derive a method for assigning a compositional type to an object based on its (Y - J), (J - Ks), and (H - Ks) colors. Methods: We present a taxonomic classification for 18 265 asteroids from the MOVIS catalog, using a probabilistic method and the k-nearest neighbors algorithm. Because our taxonomy is based only on NIR colors, several classes from Bus-DeMeo were clustered into groups and a slightly different notation was used: i.e., the superscript indicates that the classification was obtained based on the NIR colors and the subscript indicates possible misidentifications with other types. Our results are compared with the information provided by the Sloan Digital Sky Survey (SDSS) and Wide-field Infrared Survey Explorer (WISE). Results: The two algorithms used in this study give a taxonomic type for all objects having at least (Y - J) and (J - Ks) observed colors. A final classification is reported for a set of 6496 asteroids based on the criteria that kNN and probabilistic algorithms gave the same result, and the color errors are within the limits (Y - J)err ≤ 0.118 and (J - Ks)err ≤ 0.136. This set includes 144 bodies classified as Bkni, 613 as Cni, 197 as Cgxni, 91 as Xtni, 440 as Dsni, 665 as Klni, 233 as Adni, 3315 as Sni, and 798 as Vni. We report the albedo distribution for each taxonomic group and we compute new median values for the main types. We found that V-type and A-type candidates have identical size frequency distributions, but V types are five times more common than A types. Several particular cases, such as the A-type asteroid (11616) 1996 BQ2 and the S-type (3675) Kematsch, both in the Cybele population, are discussed. Classification table for 18 265 asteroids is 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/617/A12