  Let $(g, X)$ be a K\"ahler-Ricci soliton on a complex manifold $M$. We prove
that if the K\"ahler manifold $(M, g)$ can be K\"ahler immersed into a definite
or indefinite complex space form of constant holomorphic sectional curvature
$2c$, then $g$ is Einstein. Moreover, its Einstein constant is a rational
multiple of $c$.
