We show that in supersymmetric left-right models (SUSYLR), the upper bound on the lightest neutral Higgs mass can be appreciably higher than that in minimal supersymmetric standard model (MSSM). The exact magnitude of the bound depends on the scale of parity restoration and can be 10-20 GeV above the MSSM bound if mass of the right-handed gauge boson $W_R$ is in the TeV range. An important implication of our result is that since SUSYLR models provide a simple realization of seesaw mechanism for neutrino masses, measurement of the Higgs boson mass could provide an independent probe of a low seesaw scale.