A prosthesis for a cardiac atrio-ventricular valve, comprising valve leaflets, comprises a support structure (210) having a peripheral wall which defines a through-hole, The prosthesis also comprises a valve structure which is supported by the support structure (210) and which comprises prosthetic leaflets (220a-220c) which are configured to selectively close the through-hole of the support structure (210) so as to restore, during use, the functionality of a unidirectional valve. The prosthesis also comprises an anchoring member (225). The anchoring member (225) and the support structure (210) are configured so as to be coupled each other, after implantation in the body of a patient, co-operating in order to entrap and lock the valve leaflets (135a - 135b) of the cardiac atrio-ventricular valve of the patient between the peripheral wall of the support structure (210) and the anchoring member (225) so as to keep the prosthesis (200) in position. A seating (230) is defined on the support structure (210), conjugate to the anchoring member (225). The support structure (210) and the anchoring member (225) are configured and have dimensions so that they are connected with interference so as to lock the anchoring member (225) in the seating (230).