Magnetic force microscopy and spectroscopy are used to study two-dimensional islands of spherical $21\text{\ensuremath{-}}\mathrm{nm}$ magnetite nanoparticles. The observed repulsion of the magnetic tip at the edges of the islands is a clear sign of magnetic ordering: strong magnetic dipole-dipole interactions cause blocking of the nanoparticle dipole moments. These moments will be shown to form flux-closure structures, which is the origin of the magnetic contrast in dense two-dimensional magnetic nanoparticle assemblies.