In a statement released by Kennedy's office, Aulisi said: "After testing, we believe the incident was brought on by simple fatigue."
Kennedy will remain at the hospital overnight for observation and go home in the morning.
Sen. Jay Rockefeller, D-W., Va., told reporters that Obama noticed when Kennedy became ill, and rushed over to his table.
"There was a call for silence throughout the room," he said. "The president went over immediately. The lights went down, just to reduce the heat, I think."
In his remarks, Obama said his prayers were with the stricken senator, his family and wife, Vicki.
"He was there when the Voting Rights Act passed, along with John Lewis who was a warrior for justice," the newly inaugurated president said.
"And so 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," Obama said.
"It looked like a seizure," said Sen. Orrin Hatch, R-Utah, who said he was with Kennedy until they reached the ambulance.
Kennedy has suffered previous seizures since he became ill and underwent surgery last summer.
