Transistors based on two-dimensional (2D) materials are on the roadmap for the beyond 1 nm logic technology node1. This stems from their ultrathin thickness and defect-free surfaces, granting remarkable electrostatic gate control2–5. The physical channel length of 2D transistors may eventually reach <10 nm for advanced node devices. However, the equally important scaling limit for metal contacts remains unknown because of the lack of technology to directly probe the carrier injection region in contact areas. Here we use cross-sectional scanning tunnelling microscopy to directly measure the carrier transfer length as approximately 2.0 nm at the contact region of a bismuth-contacted monolayer MoS2 transistor. This approach allows contact scaling constraints to be determined, providing information for the development of future ultra-scaled electronic devices.