Fitzgibbon first came to prominence as a member of the Cork minor hurling team in the early 1980s. He won a Munster medal at this level in 1985, before later collecting an All-Ireland following a victory over Wexford. Three years later in 1988 Fitzgibbon won a Munster title with the under-21 team. Once again he later collected an All-Ireland title following a defeat of Kilkenny.
By this stage Fitzgibbon had already joined the Cork senior team. He made his debut in 1986 and collected his first senior Munster title that year. Unfortunately, Fitzgibbon missed the team’s subsequent All-Ireland final victory over Galway. Cork lost their provincial crown for the first time in five years in 1987, however, the team returned in 1990 with Fitzgibbon collecting a second Munster title. Cork later qualified for another All-Ireland appearance with Galway. Once again Cork were complete underdogs, however, in a thrilling and high-scoring game Cork defeated the men from the West, giving Fitzgibbon his first All-Ireland medal on the field of play. His championship performance later earned him his first of two consecutive All-Star awards. Two years later in 1992 Fitzgibbon won a third Munster title. Cork later faced Kilkenny in the championship decider, however, victory went to ‘the Cats’ on that occasion. Cork had now lost their last three All-Ireland final meetings with their arch-rivals Kilkenny, something which took the gloss off their wins over Galway. The following year Fitzgibbon added a National Hurling League medal to his collection. His inter-county hurling career ended shortly afterwards.