The hospitalization meant Carter's planned trip to Durham Tuesday evening for a book signing was cancelled.
Carter's grandson, Georgia state Sen. Jason Carter, said his 85-year-old grandfather was doing fine.
"He's definitely resting comfortably and expected to continue his book tour this week," Jason Carter said. "I haven't talked to him, but nobody in the family is concerned."
Carter said earlier on his Facebook page that his grandfather had left the hospital, but he later told The Associated Press he had the wrong information. A spokeswoman at MetroHealth hospital in Cleveland confirmed he was still there Tuesday afternoon.
Carter was a passenger on a Delta Air Lines flight from Atlanta to Cleveland when he became ill. After the plane landed, he was taken off by rescue crews, said Jackie Mayo, a spokeswoman at Cleveland Hopkins International Airport.
He was wheeled into an emergency room at MetroHealth on a stretcher and later was up and walking around, said Mary Atkins, who had taken her daughter to the hospital for medical treatment and saw Carter from a nearby room.
"He walked by the room and he was saying he was ready to go," she said. "They had Secret Service everywhere."
The Carter Center, the Atlanta-based nonprofit known for its international work on human rights and public health, said Carter was expected to resume his book tour this week.
President Barack Obama, stopping at a restaurant in Albuquerque, N.M., said he planned to call Carter to see how he is.
About 500 people had waited in line Tuesday afternoon at Joseph-Beth Booksellers in suburban Cleveland, where Carter was scheduled to sign copies of his new book, "White House Diary." The event was later canceled, as was a Tuesday night appearance at the Regulator Bookshop in Durham, N.C., according to his publisher.
"It's crazy for an 85-year-old guy to fly ... just to sign some books," said Regulator Bookshop co-owner John Valentine. "He's a brave guy. His health is most important."
Carter expected to continue the book tour later this week and was next scheduled to appear at two events in Washington, D.C., including one at the Smithsonian Institution, said Kathy Daneman, publicity manager at publisher Farrar, Straus & Giroux.
In the book, Carter said he pursued an overly aggressive agenda as president that may have confused voters and alienated lawmakers. But he said the tipping points that cost him the 1980 election were the Iran hostage crisis and the Democratic primary challenge by U.S. Sen. Ted Kennedy.
Carter, a former peanut farmer elected to the White House in 1976, has spent his recent years pursuing peace and human rights, efforts that won him the Nobel Peace Prize in 2002.