Which elbow injury is typically caused by hyperextension during a fall?

The injury typically associated with hyperextension during a fall is an elbow dislocation. This type of dislocation often occurs when an individual extends their arm in an attempt to break a fall, leading to an unnatural force on the elbow joint, which can dislocate the bones of the elbow.

In contrast to other options, Little League Elbow primarily results from repetitive stress on the elbow during throwing activities, generally involving young athletes. Cubital tunnel syndrome stems from compression of the ulnar nerve, which can lead to symptoms but is not primarily caused by acute trauma like a fall. Volkmann's contracture is a condition resulting from a severe compromise of blood flow to the muscles of the forearm, often after a fracture or injury that has not been adequately treated, rather than hyperextension during a fall.

Thus, elbow dislocation stands out as the most directly related to the mechanism of injury described in the question.