In the apparatus and method for monitoring a vascular access (6) of an extracorporeal circuit (5; 10) of a patient, a control and calculation unit (17) varies a flow rate of a blood pump (9) predisposed to cause blood to circulate in the extracorporeal circuit. The control and calculation unit receives the pressure values in the blood withdrawal line (5) and the blood return line (10) from two pressure sensors (8, 12); the pressure values are a series of different values of the blood flow rate. The control and calculation unit processes the data gathered by means of a mathematical model which describes the variation of pressure in the vascular access as a function of the flow rate, in order to determine the blood flow rate in the vascular access. The invention detects the presence and location of a stenosis at the vascular access of a patient subjected to a hemodialysis treatment.