  To embed the seesaw mechanism in the MSSM, two or three right-handed neutrino
supermultiplets, $N_i$, have to be added to the model. In the presence of these
new superfields, the soft supersymmetry breaking potential includes a lepton
number violating mass term which is known as the neutrino $B$-term, $M
B_\nu\tilde{N}\tilde{N}/2$. In this paper, we study the effects of $B_\nu$ on
the Higgs mass parameters. Using the condition for the electroweak symmetry
breaking, we derive an upper bound on $B_\nu$ which is two orders of magnitude
stronger than the previous bounds. We also propose a simple model in which it
is natural to have large values of $B_\nu$ while the rest of the supersymmetry
breaking terms are at the TeV scale or smaller.
