She won gold in the high jump at the 1948 games in London with a US and Olympic record of 1.68 metres (5.51ft).
She was inducted to the USA Track and Field Hall of fame in 1975 and the US Olympic Hall of Fame in 2004.
Daughter Evelyn Jones said she died after a cardiac arrest.
She added that her mother had been receiving treatment for a stroke at a nursing home in recent months.
“Alice literally set the bar with her accomplishments at the 1948 Games, but Olympic champion is only part of her incredible legacy.” US Olympic Committee CEO Scott Blackmun said.
“Alice inspired generations of athletes to be their best and she will be missed,” Mr Blackmun said.
Born in Albany in 1923, the fifth of ten children, she took an interest in high jump after watching a boys track meet and trained herself in the sport using home-made equipment.
Davis was the only American woman to win a gold medal at the 1948 games.
Olympic historian David Wallechinsky said she was honoured with a 175-mile motorcade in Georgia when she returned from London.
However, the black and white audiences were segregated at her official ceremony in Albany, New York.
Recollecting her career in the 2004 interview, Davis speculated that she could have won even more Olympic medals, but the Olympics were not held in 1940 or 1944 because of the Second World War. She retired at 25 after her London victory.
“I know I would have won in 1944, at least,” she said. “I was starting to peak then. It really feels good when Old Glory is raised and the National Anthem is played.”
Davis attended Tuskegee University and played basketball on a team that won three straight conference basketball titles.
She won 25 national athletics championships – including 10 consecutive high jump titles – between 1939 and 1948, according to USA Track and Field.
Growing up in the Deep South during the era of segregation, Davis had to overcome multiple challenges.
The New Georgia Encyclopedia recalls how she was banned from using public sports facilities because of her race, so she used whatever equipment she could cobble together to practise her jumping.
“My dad did not want me to travel to Tuskegee and then up north to the Nationals,” she said. “He felt it was too dangerous. Life was very different for African-Americans at that time.
“But I came back and showed him my medal and talked about all the things I saw. He and my mom were very proud of me.”
Davis won her first national high jump title at 16 and worked as a teacher and athletics coach after retiring.
She married Frank Davis and was the mother of two children.
Albany State University athletic director Richard Williams said: “We will continue to honour her legacy within the athletic department.”