Cross-diffusion phenomena are experimentally shown to be able to induce convective fingering around an initially stable stratification of two microemulsions with different compositions. Upon diffusion of a salt that entrains 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 provides an explanation for the mechanism of the buoyancy-driven hydrodynamic instability and for the properties of the convective fingers.