The anisotropic rare earth magnet powder of the present invention includes powder particles having R2TM14B1-type crystals of a tetragonal compound of a rare earth element (R), boron (B), and a transition element (TM) having an average crystal grain diameter of 0.05 to 1 μm, and enveloping layers containing at least a rare earth element (R′) and copper (Cu) and enveloping surfaces of the crystals. Owing to the presence of the enveloping layers, coercivity of the anisotropic rare earth magnet powder can be remarkably enhanced without using a scarce element such as Ga and Dy.