Kirkwood was a member of the Ireland team that were silver medallists at the 1978 EuroHockey Junior Championship. Other members of the team included Martin Sloan, Billy McConnell and Stephen Martin. He made his senior debut for Ireland at the age of 18 in 1981. He subsequently represented Ireland at the 1987, 1991 and 1995 Men's EuroHockey Nations Championships. He also represented Ireland at the 1990 Men's Hockey World Cup. During the latter tournament, during a match against Canada, Kirkwood sustained a horrific injury when he felt the full force of an opponents stick in his face. He was taken to hospital and missed the rest of the tournament. In 2014 Kirkwood was inducted into the Irish Hockey Association Hall of Fame.