We present Hubble Space Telescope (HST) Wide Field Camera 3 UV and near-IR (nIR) imaging of 21 Superluminous Supernovae (SLSNe) host galaxies, providing a sensitive probe of star formation and stellar mass within the hosts. Comparing the photometric and morphological properties of these host galaxies with those of core-collapse supernovae (CCSNe) and long-duration gamma-ray bursts (LGRBs), we find SLSN hosts are fainter and more compact at both UV and nIR wavelengths, in some cases we barely recover hosts with absolute magnitude around M_V_~=-14. With the addition of ground based optical observations and archival results, we produce spectral energy distribution fits to these hosts, and show that SLSN hosts possess lower stellar mass and star formation rates. This is most pronounced for the hydrogen deficient Type-I SLSN hosts, although Type-II H-rich SLSN host galaxies remain distinct from the bulk of CCSNe, spanning a remarkably broad range of absolute magnitudes, with ~30 per cent of SLSNe-II arising from galaxies fainter than M_nIR_~-14. The detection of our faintest SLSN hosts increases the confidence that SLSNe-I hosts are distinct from those of LGRBs in star formation rate and stellar mass, and suggests that apparent similarities in metallicity may be due to the limited fraction of hosts for which emission line metallicity measurements are feasible. The broad range of luminosities of SLSN-II hosts is difficult to describe by metallicity cuts, and does not match the expectations of any reasonable UV-weighted luminosity function, suggesting additional environmental constraints are likely necessary to yield hydrogen rich SLSNe.