O'Dwyer made his debut with the Tipperary senior team during the 1908 championship. He was a regular member of the starting fifteen over the next few years and won a set of All-Ireland and Munster medals in his debut season. O'Dwyer was also included on the Tipperary team that toured Belgium as part of a pan-Celtic initiative in 1910.
O'Dwyer retired from inter-county hurling following the conclusion of the 1911 championship.
After his ordination to the priesthood in 1912, O'Dwyer completed his B.A. and D.D. and served as a professor at St. Patrick's College. In 1920 he joined the Maynooth Mission to China, eventually rising to the position of Superior General in 1924. He held this post until 1947.
At the time of his death on 13 February 1975, O'Dwyer was the last surviving member of the 1908 Tipperary All-Ireland-winning team.