Cross-diffusion phenomena are shown experimentally to be able to induce convective fingering around an initially statically stable stratification of two microemulsions having a different composition. Upon diffusion of a salt entraining water and AOT micelles by cross-diffusion, the miscible interface deforms into fingers following the build-up of a non monotonic density profile in the gravitational field. A diffusion model incorporating cross-diffusion effects allows to explain the mechanism of the buoyancy-driven hydrodynamic instability and the properties of the convective fingers.