Wood grew up in an integrated neighborhood, learned to play stickball and baseball as a youth, and graduated from Thomas Jefferson High School in 1955.

Jake made his major league debut at age 23 on the Tigers' season-opener on April 11, 1961, starting at second base and batting leadoff in a 9–5 home loss to the Cleveland Indians.

Facing Indians pitcher Jim Perry for the fourth time in the game during the seventh inning, the hard-hitting Wood collected his first career hit in a big way with a two-run home run that scored Bobo Osborne.

On June 23, 1967, during his seventh season with the Tigers, his contract was purchased by the Reds, for whom he played 16 games, with his final major league career appearance coming on August 11, 1967.

He also mentors inmates at the Escambia County, Florida jail as part of the "A Will and a Way" ministry, and he participates in Tigers' reunions, autograph shows, and fantasy camps as well as Negro leagues events.