Southampton, Hampshire born inside right and centre forward Arthur Wood began his career with local clubs St Mary’s Athletic in 1909 and Eastleigh Athletic in 1910 before joining Second Division club Fulham in 1911. He made his Football League debut at Clapton Orient in April 1912 but was only a fringe player over his four seasons at Craven Cottage, making just 21 first team appearances for The Cottagers playing as either an inside right or at centre forward, scoring once which came in a 1-0 win over Bristol City at Ashton Gate in April 1914. His playing career was interrupted by the onset of the First World War which forced the suspension of peacetime football in May 1915, during which he saw active service with the Armed Forces. During the War he suffered an injury which necessitated the insertion of a metal plate into his forehead. This meant that, although he was able to resume his football career after the War, he was never again able to head the ball.
In August 1919 Wood resumed his playing career when he signed for Gillingham, then of the Southern League. In his first season with the club, he was top scorer with fourteen goals. At the end of the 1919-20 season, the club was elected into the newly formed Third Division, and Wood went on to make 53 appearances for The Gills at this level, scoring 11 times. He left Gillingham in 1922 and had a short spell with Scottish club Hamilton Academical, joining them that summer, and also briefly played for non league Northfleet before returning to Football League action with Newport County in November 1922, for whom he played 13 times scoring 3 goals in 1922-23 including a goal on his Exiles debut against Queen’s Park Rangers. His final professional club was Queen’s Park Rangers, for whom he made 20 appearances without scoring between 1923 and 1925. After retiring from professional football he worked at the Regent Palace Hotel and played for the hotel’s staff football team.