Carpenter was 88. He died due to lingering complications from a stroke he had in September, his daughter Kristen Stoever said.
"We're all shocked," Stoever said of her father's passing. "And sad ... but filled with admiration."
Carpenter and John Glenn were the only surviving astronauts from the original Mercury Seven, the men chosen by NASA to go into space.
At first, Carpenter served as a capsule communicator during Glenn's first flight. He went into orbit for the next mission, Aurora 7, when he became the fourth American in space.
"He had a long life," Stoever said. "He conquered air, space and sea."