Damien, the youngest of fifteen children, currently plays his club hurling and football with 'the Rovers' and is following in the footsteps of his brothers Mark, Tom, Séamus, John, Martin, Gerard, Noel, Paddy and Fran.
In early 1993 Fitzhenry made his senior debut in the National Hurling League quarter-final against Westmeath.
In the final of that competition Wexford drew with arch rivals and All-Ireland champions Kilkenny and there was hope of success.
Wexford later defeated Galway in the penultimate game of the championship, setting up an All-Ireland final meeting with Limerick.
Tom Dempsey was the hero of the day as he scored a goal after nineteen minutes to give Wexford a major advantage.
A 2–14 to 1–11 victory secured a safe passage to the All-Ireland semi-final where Tipperary, the defeated Munster finalists, provided the opposition.
This allowed Wexford to advance to the All-Ireland semi-final, however, Cork claimed the victory in the penultimate stage of the championship.
In 2007 Wexford lost the provincial final by double scores to Kilkenny, however, the team later shocked Tipperary in the All-Ireland quarter-final.
Fitzhenry scored a crucial goal in that game to secure the victory and set up an All-Ireland semi-final with Kilkenny.
An All-Ireland quarter-final meeting with Waterford, in spite of a great display by Fitzhenry, resulted in a 2–19 to 3–15 defeat.
Two days later there were rumours that Fitzhenry was thinking about retirement from inter-county hurling after 15 years on the panel though in January 2009 after the former Tippperary hurler Colm Bonnar was appointed as the manager two months ago.
Fitzhenry returned to the panel but did not play until their championship opening against Offaly on 30 May where he made a few magnifciant saves including a penalty from Shane Dooley.