Let X be a C' fuzzy manifold and p be a point in X. At first, it is given that the tangent space at p denoted by 7'p(^) is a vector space. İn this paper, constructing the tangent bundle nx}= V T(X)on X, it is shown that there is a covariant functor from the category of C‘ fuzzy manifolds and fuzzy differentiable functions to the category of the tangent bundles on C' fuzzy manifolds and fuzzy manifold derivative functions.