First principles calculations based on the generalized gradient approximation to the density functional theory reveal the existence of two nearly degenerate isomeric forms of Mn-13 cluster. The lowest energy structure corresponds to icosahedric packing that lies 0.65 eV lower than a caged structure with a hexagonal close-packed motif. Magnetically, however, these two isomers are very different: while the icosahedric structure is ferrimagnetic with a total magnetic moment of 33 mu(B), the hexagonal close-packed structure is a de facto antiferromagnet with a magnetic moment of 17 mu(B). The two isomers also have different ionization potentials, 5.19 and 4.82 eV, in good agreement with experiment.