Red blood cells (RBCs) are characterized by a remarkable elasticity, which allows them to undergo very large deformation when passing through small vessels and capillaries. This extreme deformability is altered in various clinical conditions, suggesting that the analysis of red blood cell (RBC) mechanics has potential applications in the search for non-invasive and cost-effective blood biomarkers. Here, we provide a comparative study of the mechanical response of RBCs in patients with Alzheimer’s disease (AD) and healthy subjects. For this purpose, RBC viscoelastic response was investigated using atomic force microscopy (AFM) in the force spectroscopy mode. Two types of analyses were performed: (i) a conventional analysis of AFM force–distance (FD) curves, which allowed us to retrieve the apparent Young’s modulus, E; and (ii) a more in-depth analysis of time-dependent relaxation curves in the framework of the standard linear solid (SLS) model, which allowed us to estimate cell viscosity and elasticity, independently. Our data demonstrate that, while conventional analysis of AFM FD curves fails in distinguishing the two groups, the mechanical parameters obtained with the SLS model show a very good classification ability. The diagnostic performance of mechanical parameters was assessed using receiving operator characteristic (ROC) curves, showing very large areas under the curves (AUC) for selected biomarkers (AUC > 0.9). Taken all together, the data presented here demonstrate that RBC mechanics are significantly altered in AD, also highlighting the key role played by viscous forces. These RBC abnormalities in AD, which include both a modified elasticity and viscosity, could be considered a potential source of plasmatic biomarkers in the field of liquid biopsy to be used in combination with more established indicators of the pathology.