Sodium clusters formed in the regular nanospace of sodalite (aluminosilicate zeolite) are known to show antiferromagnetic order without any magnetic elements. The clusters are arrayed in a body centered cubic structure. We have performed a neutron diffraction study and succeeded in detecting the magnetic Bragg peaks of the s-electron spins for the first time. The observation of both 001 and 111 magnetic reflections confirms the antiferromagnetic order with the antiparallel coupling between the nearest neighbor clusters. The magnetic form factor was examined by analyzing the intensity ratios of the magnetic and nuclear Bragg peaks. The result is in good agreement with the shape of the s-electron wave function derived from theoretical studies of the sodium nanoclusters in the cages.