Reliable neutron star mass measurements are key to determining the equation of state of cold nuclear matter, but such measurements are rare. Black widows and redbacks are compact binaries consisting of millisecond pulsars and semi-degenerate companion stars. Spectroscopy of the optically bright companions can determine their radial velocities, providing inclination-dependent pulsar mass estimates. Although inclinations can be inferred from subtle features in optical light curves, such estimates may be systematically biased due to incomplete heating models and poorly understood variability. Using data from the Fermi Large Area Telescope, we have searched for gamma-ray eclipses from 49 spider systems, discovering significant eclipses in 7 systems, including the prototypical black widow PSR B1957+20. Gamma-ray eclipses require direct occultation of the pulsar by the companion, and so the detection, or significant exclusion, of a gamma-ray eclipse strictly limits the binary inclination angle, providing new robust, model-independent pulsar mass constraints. For PSR B1957+20, the eclipse implies a much lighter pulsar (1.81 ± 0.07 solar masses) than inferred from optical light curve modelling.