We describe equivalence classes of indecomposable exact module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [11 Natale, S. (2017). On the equivalence of module categories over a group-theoretical fusion category, SIGMA, Symmetry Integrability Geom. Methods Appl. 13 Paper 042:9. p. DOI: 10.3842/SIGMA.2017.042.[Crossref] , [Google Scholar]].