  A bound on the CPT-odd four vector coefficient $k^\mu_\phi$ that appears in
Higgs sector of the Minimal Standard Model Extended (MSME) is presented. The
analysis is based on the contributions arising from the sector in question to
the anomalous dipole moment for leptons calculated at the one loop level, for
which an analytical expression is obtained. The largest contribution of this
Lorentz violating coefficient is on the lightest lepton, which results as a
consequence of a strong non-decoupling effect. By using the experimental
uncertainty of the electron anomalous dipole moment we predict that $|k^2_{
\phi\,R}|<3.29\times 10^{-29}$ GeV$^2$.
