  We consider the leptophobic $Z^\prime$ model which can appear naturally in
the flipped SU(5) or string-inspired $E_6$ models. This model can be
constrained by measurements of the $B\to M \nu\bar{\nu}$ decays and $\Delta
m_s$. We find that although the latter give much stronger constraints on the
coupling than the former, they are complementary to each other.
