Based on density-functional theory, the electronic structures and magnetism of 3d transition metal (TM)-doped arsenene nanosheets are investigated by means of first-principles methods. The results show that Sc- and Co-doped arsenene nanosheets possess the nonmagnetic semiconducting properties, while Ti, Cr, and Cu substituting As atom can induce dilute magnetic semiconductor phase. Moreover, half-metal properties are induced in the V-, Mn-, Fe-, and Ni-doped arsenene nanosheets. In addition, results also show that Ti-, V-, Mn-, and Fe-doped arsenene nanosheets present ferromagnetic coupling, whereas Cr substitutional doping results in an antiferromagnetic coupling under their most stable configuration. These results indicate that TM doping can tune effectively the electronic and magnetic properties in the arsenene nanosheets.