From 1939 to 1957, Kennedy played for the Chicago White Sox (1939–42, 1946–48, 1955–56, 1957), Cleveland Indians (1948–54), Baltimore Orioles (1954–55), Detroit Tigers (1956) and Brooklyn Dodgers (1957).

On June 22, 1937, the night before the White Sox signed him, Kennedy was working as a 16-year-old popcorn vendor at Comiskey Park during the World Heavyweight Boxing Title between Joe Louis and James J. Braddock.

At 3:36pm, Kennedy flew out to centerfield on a 2–2 pitch with two out and no one on in the 9th inning of the last Brooklyn Dodger game ever played on Sunday, September 29, 1957 at Connie Mack Stadium in Philadelphia.

This game marked his major league debut as a starter and was the only time all season Brooklyn lost to a lefthander.

Following his retirement, he was a scout and farm system director for the Indians,[2] and manager of the Triple-A Salt Lake City Bees.

The Cubs had experimented with having a committee of coaches run the team on the field since 1961, as opposed to having a single manager.

However, after the 1962 season ended with what is still the worst record in franchise history, owner Phil Wrigley named Kennedy as "head coach" for an indefinite period.

After Kennedy led the 1963 Cubs to their first winning record in 17 years, he began to assert a more traditional managerial authority over the team.

According to the 1972 book Mustache Gang, authored by Ron Bergman, on the last day of the season Kennedy walked into Charlie Finley's office, expecting an extension.