  UV luminosity functions provide a wealth of information on the physics of
galaxy formation in the early Universe. Given that this probe indirectly tracks
the evolution of the mass function of dark matter halos, it has the potential
to constrain alternative theories of structure formation. One of such scenarios
is the existence of primordial non-Gaussianity at scales beyond those probed by
observations of the Cosmic Microwave Background. Through its impact on the halo
mass function, such small-scale non-Gaussianity would alter the abundance of
galaxies at high redshifts. In this work we present an application of UV
luminosity functions as measured by the Hubble Space Telescope to constrain the
non-Gaussianity parameter $f_\mathrm{NL}$ for wavenumbers above a cut-off scale
$k_{\rm cut}$. After marginalizing over the unknown astrophysical parameters
and accounting for potential systematic errors, we arrive at a $2\sigma$ bound
of $f_{\rm NL}=71^{+426}_{-237}$ for a cut-off scale $k_{\rm
cut}=0.1\,\mathrm{Mpc}^{-1}$ in the bispectrum of the primordial gravitational
potential. Moreover, we perform forecasts for the James Webb Space Telescope
and the Nancy Grace Roman Space Telescope, finding an expected improvement of a
factor $3-4$ upon the current bound.
