John Fulton "Abe" Woods (January 18, 1898 – October 4, 1946) was a professional baseball pitcher. He appeared in one game in Major League Baseball for the Boston Red Sox during the 1924 season. Listed at 6' 0", 175 lb (79 kg)., Woods batted and threw right-handed. A native of Princeton, West Virginia, he attended West Virginia University, where he played college baseball for the Mountaineers from 1920–1923. Woods went on to become Chief of Police in Norfolk, Virginia in March 1938.