The structures and magnetic properties of Mn clusters containing 13, 15, 19 and 23 atoms have been predicted from ab initio electronic structure calculations. The lowest energy structures of the 13-, 19- and 23-atom clusters are icosahedral and have ordered spin configurations in which blocks of ferromagnetically coupled spins are antiferromagnetically coupled with each other. The 15-atom cluster is body-centered cubic with antiferromagnetic coupling. The net moments are small and lie in the range of (formula presented) however, the average local atomic moments have high values close to (formula presented) These results are discussed in light of recent Stern-Gerlach experiments. {\textcopyright} 2002 The American Physical Society.