Minimal polynomial of an exponential automorphism of $\mathbb{C}^n$

We show that the minimal polynomial of a polynomial exponential automorphism $F$ of $\mathbb{C}^n$ (i.e. $F=\exp(D)$ where $D$ is a locally nilpotent derivation) is of the form $\mu_F(T)=(T-1)^d$, with $d=\min\{m\in\mathbb{N}: D^{\circ m}(X_i)=0$ for $i=1,\ldots,n\}$.