"I have to be honest," Kennedy's wife Victoria said in a statement, "we've been pitched a real curveball. Rest assured, this is only the first inning."
"He remains in good spirits and full of energy," the doctors for the 76-year-old Massachusetts Democrat said in a statement.
They said tests conducted after the seizure showed a tumor in Kennedy's left parietal lobe. Preliminary results from a biopsy of the brain identified the cause of the seizure as a malignant glioma, they said.
His treatment will be decided after more tests but the usual course includes combinations of radiation and chemotherapy.
Nationally known brain cancer expert Dr. Maciej Lesniak from the University of Chicago told CBS News Radio that chemo and radiation very often are ineffective, and certainly don't cure this type of tumor. He also puts the average survival time at just over a year. He says often the discovery of this type of tumor is the "tip of the iceberg" - an indication that there are other cancer cells existing in the brain or elsewhere.
Dr. Lynne Taylor, a neuro-oncoloist and a member of the American Academy of Neurology, advises there are some potentially critical pieces of information aren't publicly known. Taylor told CBS that the size, grade and location of the tumor would all be factors in Kennedy's treatment.
"It could be too big and in a location, that means surgery can't be done, or get it all," she said. "It could be, given the exact location, surgery could cause severe problems, including the loss of the ability to communicate."
Kennedy has been hospitalized in Boston since Saturday, when he was airlifted from Cape Cod after a seizure at his home.
Kennedy's father-in-law told CBS station WBZ-TV on Monday that the senator had suffered two seizures before reaching the hospital. Only one has been reported by officials.
WBZ said Kennedy had the second seizure during the helicopter ride to Mass. General, according to father-in-law, Edmund Reggie.
"He has had no further seizures, remains in good overall condition, and is up and walking around the hospital," said the statement by Dr. Lee Schwamm, vice chairman of the Department of Neurology at Massachusetts General Hospital and Dr. Larry Ronan, Kennedy's primary care physician.
They said Kennedy will remain in the hospital "for the next couple of days according to routine protocol."
Kennedy's wife and children have been with him each day since he was hospitalized. Senator Kennedy's son, Rep. Patrick Kennedy, D-R.I., plans to stay at the hospital for the time being.
"Obviously it's tough news for any son to hear," said spokeswoman Robin Costello. "He's comforted by the fact that his dad is such a fighter, and if anyone can get through something as challenging as this, it would be his father. So he's optimistic, he's hopeful, but obviously he's concerned."
President Bush was notified by his staff of Kennedy's diagnosis at 1:20 p.m.
CBS News White House correspondent Mark Knoller reports that after Kennedy helped enact the No Child Left Behind program, President Bush was full of praise for him.
"He is a fabulous United States senator," the president said. "When he's against you, it's tough. When he's with you, it is a great experience."
Now, after learning of Kennedy's condition, Mr. Bush issued a statement calling Kennedy his friend and a man of tremendous courage. He said he prays for his full recovery.
the president told Kennedy's wife on Monday, according to Kennedy spokeswoman Stephanie Cutter.
Malignant gliomas are a type of brain cancer diagnosed in about 9,000 Americans a year - and the most common type among adults. It's an initial diagnosis: How well patients fare depends on what specific tumor type is determined by further testing.
Average survival can range from less than a year for very advanced and aggressive types - such as glioblastomas - or to about five years for different types that are slower growing.
CBS News correspondent Randall Pinkston reports that in the Senate, where Kennedy has served more than 40 years, the news shook his colleagues to the core - on both sides of the aisle.
"Thank God for you, Ted, thank God for you," said a visibly distraught Senator Robert Byrd D-W.Va., the only member who has served longer in the Senate than Kennedy.
"I'm really sad," former Sen. Bob Kerrey, D-Neb., said when told in a Senate hallway about Kennedy's condition. "He's the one politician who brings tears to my eyes when he speaks."
"I am so deeply saddened I have lost the words," Sen. John Warner, R-Va., said in a Senate hallway. Warner said he and Kennedy had been friends for 40 years. Both served on the Senate Armed Services Committee together.
"You know like Churchill once said in the darkest days of the battle, Britain - never, never, never give in," Warner said later speaking to his congressional colleages, "and those words are in Ted Kennedy's mind right now. He'll take on this challenge."
"I have said on numerous occasions, I have described Ted Kennedy as the last lion in the Senate," said Republican presidential hopeful John McCain. "And I have held that view because he remains the single most effective member of the Senate if you want to get results. He is not reluctant to share the credit. And when he fails, he is willing to take the blame."
Kennedy's family continues to remain positive. In a photo released Tuesday afternoon, the smiling senator is shown with his family in the hospital.
In her upbeat public statement, Victoria Kennedy said, "Teddy is leading us all as usual, in his calm approach to getting the best information possible."
Kennedy, the second-longest serving member of the Senate and a dominant figure in national Democratic Party politics, was elected in 1962, filling out the term won by his brother, John F. Kennedy.
His eldest brother, Joseph, was killed in a World War II airplane crash. President Kennedy was assassinated in 1963 and his brother Robert was assassinated in 1968.
Kennedy is active for his age, maintaining an aggressive schedule on Capitol Hill and across Massachusetts. He has made several campaign appearances for Sen. Barack Obama in February, and most recently last month.
Kennedy, the senior senator from Massachusetts, was re-elected in 2006 and is not up for election again until 2012.
Were he to resign or die in office, state law requires a special election for the seat no sooner than 145 days and no later than 160 days after the vacancy occurs.