The presence of substructures in dark matter haloes is an unavoidable consequence of the cold dark matter paradigm. Indirect signals from these objects have been extensively searched for with cosmic rays and γ rays. At first sight, Cherenkov telescopes seem not very well suited for such searches, due to their small fields of view and the random nature of the possible dark matter substructure positions in the sky. However, with long enough exposure and an adequate observation strategy, the very good sensitivity of this experimental technique allows us to constrain particle dark matter models. We confront here the sensitivity map of the HESS experiment built out of their Galactic scan survey to the state-of-the-art cosmological N-body simulation Via Lactea II. We obtain competitive constraints on the annihilation cross section, at the level of 10-24-10-23cm3s-1. The results are extrapolated to the future Cherenkov Telescope Array, in the cases of a Galactic plane survey and of an even wider extragalactic survey. In the latter case, it is shown that the sensitivity of the Cherenkov Telescope Array will be sufficient to reach the most natural particle dark matter models.