Hubbell was born in Carthage, Missouri, to Margaret Dell (née Upp) and George Owen Hubbell, and was one of seven children. He was raised in Meeker, Oklahoma, where he attended Meeker High School.

After graduating from high school, Hubbell worked for an oil company and played for their baseball team which encouraged him to play professionally.

In the 1934 All Star Game played at the Polo Grounds, Hubbell produced one of baseball's most memorable moments by striking out five future Hall of Famers in succession: Babe Ruth, Lou Gehrig, Jimmie Foxx, Al Simmons and Joe Cronin. In 1984, the 50th anniversary of this legendary performance, Hubbell was on hand for the 1984 All-Star Game at San Francisco's Candlestick Park to throw out the first pitch, which was a screwball.

Hubbell was married to Lucille "Sue" Harrington (1905–1967) from 1930 until her death. They had two children: Carl Jr. (born 1936) and James. Carl Jr. had a brief career in the lower minor leagues and later was a career officer in the United States Marine Corps.

Hubbell suffered a stroke while driving near his home in Mesa, Arizona, on November 19, 1988, that caused him to lose control of his car and crash into a lamppost. He was taken to a hospital in Scottsdale, where he died of blunt force injuries two days later. He is interred at Meeker-Newhope Cemetery in Meeker, Oklahoma. His death came exactly 30 years after that of his teammate Mel Ott, who likewise died from injuries sustained in an automobile accident.