  We introduce and study the new notion of an {\em exact factorization}
$\mathcal{B}=\mathcal{A}\bullet \mathcal{C}$ of a fusion category $\mathcal{B}$
into a product of two fusion subcategories $\mathcal{A},\mathcal{C}\subseteq
\mathcal{B}$ of $\mathcal{B}$. This is a categorical generalization of the well
known notion of an exact factorization of a finite group into a product of two
subgroups. We then relate exact factorizations of fusion categories to exact
sequences of fusion categories with respect to an indecomposable module
category, which was introduced and studied by P. Etingof and the author in
\cite{EG}. We also apply our results to study extensions of a group-theoretical
fusion category by another one, provide some examples, and propose a few
natural questions.
