  We introduce the notion of the modular class of a Lie algebroid equipped with
a Nambu structure. In particular, we recover the modular class of a
Nambu-Poisson manifold $M$ with its Nambu tensor $\Lambda$ as the modular class
of the tangent Lie algebroid $TM$ with Nambu structure $\Lambda.$ We show that
many known properties of the modular class of a Nambu-Poisson manifold that of
a Lie algebropid extend to the setting of a Lie algebroid with Nambu structure.
Finally, we prove that for a large class of Nambu-Poisson manifolds considered
as tangent Lie algebroids with Nambu structures, the associated modular classes
are closely related to Evens-Lu-Weinstein modular classes of Lie algebroids.
