The physical processes by which gas is accreted onto galaxies, transformed into stars, and then expelled from galaxies are of paramount importance to galaxy evolution studies. Observationally constraining each of these baryonic components in the same system, however, is challenging. Furthermore, simulations indicate that the stellar mass of galaxies is a key factor influencing CGM properties. Indeed, absorption lines detected against background quasars offer the most compelling way to study the cold gas in the circumgalactic medium (CGM). The MUSE-ALMA Haloes survey is composed of quasar fields covered with VLT/MUSE observations, comprising 32 H I absorbers at 0.2 < z < 1.4 and 79 associated galaxies, with available or upcoming molecular gas measurements from ALMA. We use a dedicated 40-orbit HST UVIS and IR WFC3 broad-band imaging campaign to characterize the stellar content of these galaxies. By fitting their spectral energy distribution, we establish they probe a wide range of stellar masses: 8.1 < log (M_∗/M_⊙) < 12.4. Given their star formation rates, most of these objects lie on the main sequence of galaxies. We also confirm a previously reported anticorrelation between the stellar masses and CGM hydrogen column density N (H I), indicating an evolutionary trend where higher mass galaxies are less likely to host large amounts of H I gas in their immediate vicinity up to 120 kpc. Together with other studies from the MUSE-ALMA Haloes survey, these data provide stellar masses of absorber hosts, a key component of galaxy formation and evolution, and observational constraints on the relation between galaxies and their surrounding medium.