  We prove a sharp Schwarz type inequality for the Weierstrass- Enneper
representation of the minimal surfaces. It states the following. If
$F:\mathbf{D}\to \Sigma$ is a conformal harmonic parameterization of a minimal
disk $\Sigma$, where $\mathbf{D}$ is the unit disk and $|\Sigma|=\pi R^2$, then
$|F_x(z)|(1-|z|^2)\le R$. If for some $z$ the previous inequality is equality,
then the surface is an affine disk, and $F$ is linear up to a M\"obius
transformation of the unit disk.
