Bunning, who served in the U.S. Senate from 1999 to 2011, had been recovering from a stroke he suffered in 2016.
"Jim, as those within the baseball community know, is one of the most important figures in the history of the Major League Baseball Players Association", Major League Baseball Players Association executive director Tony Clark said, per ESPN.
Known as a no-nonsense pitcher who threw hard and knocked batters down when necessary, the big right-hander belonged to a rare group of major league pitchers to throw a ideal game in the modern era. He did not seek re-election in 2010.
Later moving into politics, Bunning went after his opponents with a similar velocity in his second career in Congress.
Bunning also served 12 years in the US House. "He will be missed", Rand Paul, current U.S. Senator for Kentucky, wrote on Twitter.
He belonged to a rare group of major league pitchers to throw a flawless game in the modern era.
Time magazine, in April 2006, ranked Bunning as among the nation's "five worst senators", dubbing him "the underperformer" who was hostile to his staff and showed little interest in policy unless it involved baseball.
On Saturday, McConnell released a statement saying, "Jim rarely shied away from a new adventure". He was elected to the Hall of Fame in 1996 via the Veterans Committee. "This Hall of Famer will long be remembered for many things, including a flawless game, a larger-than-life personality, a passion for Kentucky, and a loving family".
He played baseball professionally from 1955 to 1971, mostly with Detroit and Philadelphia. While spending most of his career with the Tigers and Phillies, he also had stints with the Pittsburgh Pirates and the Los Angeles Dodgers.
The side-arming Bunning enjoyed one of the greatest days of his career in Shea Stadium, firing a ideal game against the Mets on Father's Day 1964 - with his wife and daughter Barbara in the stands. He was elected to the House of Representatives in 1986 and to the Senate in 1998.