Kyle died at home on Thursday following a prolonged illness that was not specified, the Irish Rugby Football Union said on Friday.
Kyle played 46 times for Ireland in an 11-year international career, scoring seven tries, and helped the country win a grand slam in the Five Nations in 1948 — a feat that was not achieved again by the Irish until 2009 in the Six Nations.
He was also a pivotal figure in Five Nations title wins in 1949 and '51.
In 2002, he was voted Ireland's best ever rugby player in a poll by the country's union. He was inducted into the world governing body's Hall of Fame in 1999.
"Jack is a true legend and gentleman of the game," IRFU president Louis Magee said, "and he will be fondly remembered by everyone in rugby."
Kyle, who played club rugby for Ulster, represented the British and Irish Lions on their tour of New Zealand and Australia in 1950. He played in 20 of 29 games, including all six tests.
After retiring from rugby in 1963, Kyle embarked on humanitarian work in Sumatra and Indonesia and worked as a surgeon in Zambia from 1966-2000.