Mr Kennedy, 76, is conscious and talking with his family after earlier being flown from Cape Cod to Massachusetts General Hospital. His doctors have said that he did not suffer a stroke, as initially feared.
The youngest brother of assassinated President John F Kennedy, he is one of the best-known Democratic politicians. He has been an active supporter of Barack Obama for the Democratic nomination for US president.
His office said in a statement that he was “resting comfortably”. “It appears that Sen Kennedy experienced a seizure this morning,” it said. “He is undergoing a battery of tests at Massachusetts General Hospital to determine the cause of the seizure.”