  Let $X$ be an irreducible algebraic variety over $\mathbb{C}$, endowed with
an algebraic foliation ${\cal{F}}$. In this paper, we introduce the notion of
minimal invariant variety $V({\cal{F}},Y)$ with respect to $({\cal{F}},Y)$,
where $Y$ is a subvariety of $X$. If $Y=\{x\}$ is a smooth point where the
foliation is regular, its minimal invariant variety is simply the Zariski
closure of the leaf passing through $x$. First we prove that for very generic
$x$, the varieties $V({\cal{F}},x)$ have the same dimension $p$. Second we
generalize a result due to X. Gomez-Mont. More precisely, we prove the
existence of a dominant rational map $F:X\to Z$, where $Z$ has dimension
$(n-p)$, such that for every very generic $x$, the Zariski closure of
$F^{-1}(F(x))$ is one and only one minimal invariant variety of a point. We end
up with an example illustrating both results.
