At club level he played with Borris–Ileigh and was also a member of the Tipperary senior hurling team.
O'Dwyer first played hurling at juvenile and underage levels and was part of the team that won the club's inaugural Tipperary U21AHC title in 1969.
His association with the club's senior team spanned three decades, during which time he won five North Tipperary SHC titles and three Tipperary SHC titles between 1972 and 1988.
O'Dwyer was a non-playing substitute and selector when Borris–Ileigh beat Rathnure in the 1987 All-Ireland club final.
After a period away from the team he returned to make several championship appearances in 1976 and 1977.