A medical-image processing apparatus and a medical-image diagnostic apparatus according to an embodiment include an acquisition unit, a generation unit, an identification unit, and a display control unit. The acquisition unit acquires a medical image containing a blood vessel collected by the medical-image diagnostic apparatus. The generation unit generates an anatomical structure model based on the medical image acquired by the acquisition unit. The identification unit identifies a position, on the medical image, of an index relating to blood flow analyzed through fluid analysis using the anatomical structure model. The display control unit displays the position of the index on the medical image, and also displays the index associated with the position of the index on the medical image.