Kennedy, 75, plans to rest for a few days at the family's Hyannis Port compound before returning to work in the Senate, according to a statement from his office.
The blockage in Kennedy's left carotid artery, which supplies blood to the face and brain, was discovered Oct. 4 after a routine physical examination and MRI on his back.
Kennedy hurt his back in a 1964 plane crash, and an MRI is conducted periodically to check on his spine.
Dr. Richard Cambria, who performed the surgery, told reporters the surgery was performed to prevent a stroke.
He said the procedure is reserved for those with more than 70 percent blockage, and Kennedy had "a very high-grade blockage." He declined to be more specific.
One of Kennedy's doctors, Laurence Ronan, said the senator's overall health is "excellent," though Kennedy is on blood-pressure and cholesterol medication.