We have investigated the magnetic ordering and the phase transition in MnO nanoparticles confined in a porous glass using polarized neutron scattering. These MnO nanoparticles are best described as extended wormlike structures with a mean diameter of 70 Å. We observe an apparent continuous magnetic phase transition in MnO nanoparticles, in contrast to the well-known discontinuous phase transition in bulk MnO. By polarization analysis, separating the magnetic scattering, it is found that within the individual MnO nanoparticles about 60% of atoms remain disordered in the low-temperature limit, presumably due to interactions between nanoparticles and glass walls. The continuous character of the phase transition and the unusual temperature dependence suggests a surface-induced disorder phenomenon.