  Let $\mathcal{F}$ be a transversely orientable codimension one minimal
foliation without vanishing cycles of a manifold $M$. We show that if the
fundamental group of each leaf of $\mathcal{F}$ has polynomial growth of degree
$k$ for some non-negative integer $k$, then the foliation $\mathcal{F}$ is
without holonomy.
