This paper presents an aptameric graphene nanosensor for rapid and sensitive measurement of arginine vasopressin (AVP) toward continuous monitoring of critical care patients. The nanosensor is a field-effect transistor (FET) with monolayer graphene as the conducting channel and is functionalized with a new custom-designed aptamer for specific AVP recognition. Binding between the aptamer and AVP induces a change in the carrier density in the graphene and resulting in measurable changes in FET characteristics for determination of the AVP concentration. The aptamer, based on the natural enantiomer D-deoxyribose, possess optimized kinetic binding properties and is attached at an internal position to the graphene for enhanced sensitivity to low concentrations of AVP. Experimental results show that this aptameric graphene nanosensor is highly sensitive (with a limit of detection of 0.3 pM and a resolution of 0.1 pM) to AVP, and rapidly responsive (within 90 s) to both increasing and decreasing AVP concentration changes. The device is also reversable (within 4%), repeatable (within 4%) and reproducible (within 5%) in AVP measurements.