Sensors that are able to detect and track single unlabelled biomolecules are an important tool both to understand biomolecular dynamics and interactions at nanoscale, and for medical diagnostics operating at their ultimate detection limits. Recently, exceptional sensitivity has been achieved using the strongly enhanced evanescent fields provided by optical microcavities and nano-sized plasmonic resonators. However, at high field intensities photodamage to the biological specimen becomes increasingly problematic. Here, we introduce an optical nanofibre based evanescent biosensor that operates at the fundamental precision limit introduced by quantisation of light. This allows a four order-of-magnitude reduction in optical intensity whilst maintaining state-of-the-art sensitivity. It enable quantum noise limited tracking of single biomolecules as small as 3.5 nm, and surface-molecule interactions to be monitored over extended periods. By achieving quantum noise limited precision, our approach provides a pathway towards quantum-enhanced single-molecule biosensors.