  We introduce warped product skew semi-invariant submanifolds of order $1$ of
a locally product Riemannian manifold. We give a necessary and sufficient
condition for skew semi-invariant submanifold of order 1 to be a locally warped
product. We also prove that the invariant distribution which is involved in the
definition of the submanifold is integrable under some restrictions. Moreover,
we find an inequality between the warping function and the squared norm of the
second fundamental form for such submanifolds. Equality case is also discussed.
