Due to their ultra‐high sensitivity, solution‐gated graphene‐based field‐effect transistors (SG‐GFET) have been proposed for applications in bio‐sensing. However, challenges regarding the functionalization of GFETs have prevented their applications in clinical diagnostics so far. Here GFET sensors based on van der Waals (vdW) heterostructures of single‐layer graphene layered with a molecular ≈1 nm thick carbon nanomembrane (CNM) are presented. The CNM acts as an ultrathin molecular interposer between the graphene channel and the analyte and allows bio‐functionalization without impairing the graphene properties including its charge carrier mobility. To achieve specificity and reliability in the detection of biomarkers in real patient samples, the functionalization incorporates biostable aptamers in the non‐natural l‐configuration and hydrophilic polyethylene glycol for avoiding non‐specific adsorption. A rapid (≈5 min) detection of the clinically relevant inflammatory mediator CXCL8/IL‐8 within the concentration range of 0.5 – 500 pM (5 – 5000 pg ml−1) is demonstrated in nasal swab samples collected from patients with respiratory tract infections. This detection range may aid in diagnostics of early‐stage infectious diseases making the reported approach promising for the development of future medical tools.