Light quark masses are computed for Kogut-Susskind fermions by evaluating non-perturbatively the renormalization factor for bilinear quark operators. Calculations are carried out in the quenched approximation at beta = 6.0, 6.2, and 6.4. For the average up and down quark mass we find m<(MS)over bar>(2GeV) = 4.15(27)MeV in the continuum limit, which is significantly larger than 3.51(20)MeV (q(*) = 1/a) or 3.40(21)MeV (q(*) = pi/a) obtained with the one-loop perturbative renormalization factor.