Identifying abnormalities in red blood cells can provide important medical clues for the diagnosis, prognosis, and treatment of some health disorders. A common test used to examine the conditions of erythrocytes in humans is osmotic fragility. The standard technique to determine the osmotic fragility of red blood cells is laborious and time-consuming, and provides only approximate values with a few experimental data. In this work, we propose and investigate a way to measure the osmotic fragility of erythrocytes, rapidly and in a straightforward, more quantitative and less laborious way, with an optical sensor. The basic idea is monitoring in real time the refractive index of a suspension of erythrocytes to follow the kinetics of their lysis as the hemoglobin-rich cytosol is released from the erythrocytes in the surrounding hypotonic solution during hemolysis, resulting in an increase of the refractive index. We propose a device to measure in real time the refractive index and demonstrate the feasibility of monitoring the hemolysis process with high resolution. Our results show that the release of hemoglobin-rich cytosol during the progress of the hemolysis of erythrocytes in hypotonic media is generally an exponential-like function of time. We provide a mathematical model that reproduces experimental curves effectively. We show results for erythrocytes obtained from human blood stored in a blood bank and from volunteers diagnosed with two different types of anemia: hemolytic and drepanocytic. We define times, measurable from the kinetics of the refractive index signal, to quantify the progress of hemolysis as a possible new method of measuring osmotic fragility.