We measured a spin polarization above a Pt(111) surface in the vicinity of a Co nanostripe by spin-polarized scanning tunneling spectroscopy. The spin polarization exponentially decays away from the Pt-Co interface and is detectable at distances larger than 1 nm. By performing self-consistent ab initio calculations of the electronic structure for a related model system we reveal the interplay between the induced magnetic moments within the Pt surface and the spin-resolved electronic density of states above the surface.