With the generalized gradient approximation in first principle all-electron calculations, the lowest energy structures of ZnnSen (n=6-13) nanoclusters were obtained as the pristine clusters. A number of configurations and structural isomers of ZnnSen (n=6-13) nanoclusters doped with single and two Mn atoms were used to investigate the structural and magnetic properties of manganese-doped ZnnSen (n=6-13) nanoclusters. It arrives at a conclusion that Mn doping does not change the size-dependent oscillating behavior in second-order energy difference of ZnnSen (n=6-13) nanoclusters, but leads to the decrease of energy gap between lowest unoccupied molecular orbital and the highest occupied molecular orbital. Energy arguments indicate that Mn atoms prefer to substitute Zn atoms in Mn-doped ZnnSen (n=6-13) nanoclusters. Owing the Mn-Mn short-ranged superexchange mechanism, Mn atoms favor to locate at adjacent Zn atom sites in antiferromagnetic states of ZnnSen nanoclusters doped with two Mn atoms.