The best-known property of superfluid helium is the vanishing viscosity that objects experience while moving through the liquid with speeds below the so-called critical Landau velocity. This critical velocity is generally considered a macroscopic property as it is related to the collective excitations of the helium atoms in the liquid. In the present work we determine to what extent this concept can still be applied to nanometer-scale, finite size helium systems. To this end, atoms and molecules embedded in helium nanodroplets of various sizes are accelerated out of the droplets by means of optical excitation, and the speed distributions of the ejected particles are determined. The measurements reveal the existence of a critical velocity in these systems, even for nanodroplets consisting of only a thousand helium atoms. Accompanying theoretical simulations based on a time-dependent density functional description of the helium confirm and further elucidate this experimental finding.