  Let $(M^{n+1},g,e^{-f}d\mu)$ be a complete smooth metric measure space with
$2\leq n\leq 6$ and Bakry-\'{E}mery Ricci curvature bounded below by a positive
constant. We prove a smooth compactness theorem for the space of complete
embedded $f$-minimal hypersurfaces in $M$ with uniform upper bounds on
$f$-index and weighted volume. As a corollary, we obtain a smooth compactness
theorem for the space of embedded self-shrinkers in $\mathbb{R}^{n+1}$ with
$2\leq n\leq 6$. We also prove some estimates on the $f$-index of $f$-minimal
hypersurfaces, and give a conformal structure of $f$-minimal surface with
finite $f$-index in three-dimensional smooth metric measure space.
