Abeijón began his career at Uruguayan tradition Nacional Montevideo. There he played until his move to the 1997/98 season at Racing Santander. From the 1998/1999 season was Abeijón active in the Italian Serie A for Cagliari Calcio. There he remained until the 2003/04 season, when he moved briefly within the B series to Como Calcio. After ten inserts for Como, he returned to Cagliari Calcio and played there yet, until he joined in 2006/ 07 Atalanta Bergamo. For the Clausura 2008 he returned to Uruguay and played from then on for the montevideanischen club River Plate.
He graduated from his debut on 19 October 1994 until his last mission on 19 November 2003 23 caps for the Uruguay national team, where he scored a total of two goals.