A brachial plexus injury is an injury to the nerves that travel from your neck down to your arms, according to the University of Michigan Health System. The nerves linked to your spinal cord that allow your limbs to move and have sensation are called peripheral nerves. These peripheral nerves make up your brachial plexus. Exercise can help to strengthen and rehabilitate a brachial plexus injury. You should always consult your doctor before beginning an exercise program to rehabilitate your brachial plexus injury