We consider holomorphic foliations of codimension one in $\mathbb {CP}(n)$, $n\geq 3$, with a Kupka component. We prove that if the Kupka component is a complete intersection, then the foliation has a first integral of the type $f^p/g^p$ where $p,q$ are positive integers with $(p,q) = 1$, $f$ and $g$ are homogeneous polynomials in $\mathbb {C}^{n+1}$ such that $p\,\mathrm {degree}(f) = q\,\mathrm {degree}(g)$ and the Kupka component is $\{ f = g = 0\}$ in homogeneous coordinates.