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.
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