  We define the Milnor number -- as the intersection number of two holomorphic
sections -- of a one-dimensional holomorphic foliation $\mathscr{F}$ with
respect to a compact connected component $C$ of its singular set. Under certain
conditions, we prove that the Milnor number of $\mathscr{F}$ on a
three-dimensional manifold with respect to $C$ is invariant by $C^1$
topological equivalences.
