Kennedy, who has been under treatment for a brain tumor, was hospitalized for observation.
The senator's office told CBS News that Kennedy left the hospital and is headed home to get rest.
"After testing, we believe the incident was brought on by simple fatigue," Dr. Edward Aulisi, chairman of neurosurgery at Washington Hospital Center said in a statement released by the senator's office Tuesday.
The 76-year-old Massachusetts Democrat was "talking with family and friends, and feeling well," the statement said.
Kennedy's seizure was witnessed by fellow senators. Sen. Chris Dodd, D-Conn., quoted Kennedy as saying, "I'll be OK, I'll see you later" as he was put into an ambulance.
Kennedy had appeared in good health and spirits a few hours earlier when he stepped out of the Capitol and onto the inauguration platform where Mr. Obama took the oath of office.
Mr. Obama told lawmakers his prayers were with the stricken senator and his family.
"I would be lying to you if I did not say that right now a part of me is with him. And I think that's true for all of us," Mr. Obama said.
Kennedy was diagnosed last May with a particularly aggressive type of brain tumor, called a malignant glioma, after suffering a seizure at his Massachusetts home. He had surgery to remove as much as possible of the tumor, then underwent radiation and chemotherapy.
A doctor not connected with the senator's care, Dr. Matthew Ewend, neurosurgery chief at the University of North Carolina, said it's not unusual for patients recovering from brain tumors to suffer seizures.