Final answer:
The median nerve is the nerve at risk of injury in a supracondylar fracture of the humerus.
Step-by-step explanation:
In a supracondylar fracture, which is a fracture across the distal humerus above both epicondyles, the nerve at risk of injury is the median nerve. The median nerve is systemic to the arm and is located between the ulnar and radial nerves. Such injuries can potentially lead to serious complications, including ischemia due to vascular compression, and thus it's vital to assess nerve function during the management of these fractures.