President Barack Obama had honored Medicine Crow with the Presidential Medal of Freedom, the nation's highest civilian honour, in 2009.
Joe was a Crow War Chief, veteran, elder, historian, author, and educator," Bullock said in a statement announcing his death yesterday.
"His legacy will forever serve as an inspiration for all Native Americans - and all Montanans."
Medicine Crow studied anthropology in college, and for three decades worked for the Bureau of Indian Affairs. He later became the official historian of Montana's Crow Tribe.
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As an army scout in Europe he completed the four tasks needed to become a Crow War Chief: he led raids behind enemy lines, he entered an enemy camp and stole horses, he disarmed an enemy, and he touched an enemy without killing him.
"I never got a scratch," he told the Billings Gazette decades later.
His grandfather, Medicine Crow, was a warrior and scout during the 19th century Plains and Indian wars.
"My grandfather trained me to be a warrior," Joe Medicine Crow told the Indian Country Today website in 2013. "The Crow people were so-called, 'warlike.' We were a very militaristic people."
Crow Tribe chairman Darren Old Coyote described him as "a true American hero."
"He was my everything," his son Ronald Medicine Crow told the Gazette. "I don't think I will be able to fill his boots because he was able to accomplish so much in his history.