Let $X$ be a smooth complex manifold and $\phi:\; X \mapsto Y$ a proper holomorphic map which is birational ("birational contraction"), and $Z= \phi^{-1}(y)$ its fiber in a point $y$. The variety $Y$ is not assumed to be smooth. In this case I think that $Z$ is Moishezon.

I would be very grateful for a reference or a simple argument.

Misha