In the infrared fixed point (IFP) scenario of the minimal supersymmetric model (MSSM), the top-quark mass and other physical quantities of the low-energy theory are insensitive to the values of the parameters of the theory at some high energy scale. In this framework we evaluate the light CP-even Higgs mass, m h 0 , taking into account some important effects that had not been previously considered. In particular, the supersymmetric correction to the relation between the running and the physical top-quark masses lowers the value of tan β, thereby implying a lower predicted value of m h 0 . Assuming a supersymmetric threshold of M S ≤ 1 TeV and M t = 175 GeV, we find an upper bound of m h 0 ≤ 97 ± 2 GeV; the most plausible value of m h 0 lies somewhat below the upper bound. This places the Higgs boson in the IFP scenario well within the reach of the LEP-2 Higgs search.