  In the presence of non-minimal gravitational coupling $ \xi H^\dagger H {\cal
R}$ between the standard model (SM) Higgs doublet $H$ and the curvature scalar
${\cal R}$, the effective ultraviolet cutoff scale is given by $\Lambda_{\rm
cut}\approx m_P/\xi$, where $m_P$ is the reduced Planck mass, and $\xi \gtrsim
1$ is a dimensionless coupling constant. In type I and type III seesaw extended
SM, which can naturally explain the observed solar and atmospheric neutrino
oscillations, we investigate the implications of this non-minimal gravitational
coupling for the SM Higgs boson mass bounds based on vacuum stability and
perturbativity arguments. A lower bound on the Higgs boson mass close to 120
GeV is realized with type III seesaw and $\xi \sim 10-10^3$.
