"The senator is not in immediate danger," he said. Kennedy is having further tests at Massachusetts General Hospital to determine the cause of the seizures.
His wife, Victoria, two of his children and niece Caroline Kennedy are among those with him at the hospital.
In October, the senator underwent surgery for a partially blocked artery in his neck.
Kennedy is the last surviving brother of John F Kennedy, the former president who was assassinated on November 22, 1963.
His brother Robert Kennedy was assassinated on June 5, 1968, as he was campaigning for the presidency.
A critic of George Bush, the current US president, Kennedy is a supporter of Barack Obama, who is running for the Democratic nomination to contest a presidential election in November.
First elected to the senate in 1962, he is the second longest-serving senator after Robert Byrd of West Virginia.