We consider holomorphic foliations of dimension k > 1 and codimension ≥ 1 in the projective space Pn, with a compact connected component of the Kupka set. We prove that if the transversal type is linear with positive integer eigenvalues, then the foliation consists of the fibers of a rational fibration Φ: ℙn-ℙn-k. As a corollary, if dim(F) ≥cod(F) + 2 and has a transversal type diagonal with different eigenvalues, then the Kupka component K is a complete intersection and the leaves of the foliation define a rational fibration. The same conclusion holds if the Kupka set has a radial transversal type. Finally, as an application, we find a normal form for non-integrable codimension-one distributions on Pn.