Even in curved space, Minkowski space is still a good description in an infinitesimal region surrounding any point (barring gravitational singularities). More abstractly, it can be said that in the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Thus, the structure of Minkowski space is still essential in the description of general relativity.