Skowron was diagnosed with cancer a year ago. He died at a hospital in Illinois, the New York Yankees said in a statement.
Skowron was selected as an all-star five times with the New York Yankees and once while with the White Sox in his native Chicago.
He was a World Series champions five times -- 1956, 1958, 1961 and 1962 with the Yankees and 1963 when the Los Angeles Dodgers beat the Yankees in four games.
"Moose will always be remembered as being one of the key members of the Yankees' dynasties in the '50s and early '60s," said Yankees Managing General Partner Hal Steinbrenner.
"He was a winner in every sense of the word and someone the Yankees family cared deeply for. Baseball lost one of its finest ambassadors."
Skowron broke into the major leagues in 1954 with the New York Yankees and played with the Yankees for nine seasons. He also played for the White Sox, Washington Senators and Dodgers before wrapping up his career in 1967 with the California Angels.
He hit .282 over 1,658 games with 211 home runs and 888 runs batted in.
Skowron attended Purdue University on a football scholarship before focusing in baseball.