The (wrapped) Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds and which contains a wealth of information about the symplectic topology. I will discuss the construction of the wrapped Fukaya category for certain completely integrable Hamiltonian systems. These are 2n-dimensional symplectic manifolds carrying a system of n commuting Hamiltonians surjecting onto Euclidean space. This gives rise to a Lagrangian torus fibration with singularities. For dimension 3 and below and under certain assumptions about the structure of these singularities, I will show that the wrapped Fukaya category is naturally equivalent to the category of chain complexes of modules over the Floer cohomology of a Lagrangian section.