He played in Major League Baseball, primarily as a shortstop from 1963 to 1971 for the Atlanta Braves and the Cincinnati Reds.

Woodward played baseball at Coral Gables Senior High School and led the team to the 1960 Class AA state title.

He was acquired along with Tony Cloninger and Clay Carroll by the Reds from the Atlanta Braves for Milt Pappas, Bob Johnson and Ted Davidson on June 11, 1968.

[3] On July 10, 1970, Woodward hit his only major league home run in 2,423 plate appearances, a two-run shot off Ron Reed against the Atlanta Braves.

His draft picks included Alex Rodriguez, Jason Varitek, Derek Lowe, Bret Boone, and Raúl Ibañez.