It is believed the 29-year-old was attending a wedding and had an accident at a swimming pool.
He played for Eoghan Ruadh GAA club in Dungannon and at inter-county level for Tyrone senior hurling team.
The team's manager Michael McShane described Mr Casey as a true gentleman and one of the finest players he had managed. He said the team was "rocked to our very core".
Speaking to BBC Sport, he said: "His loss is incalculable; on behalf of Tyrone hurling management we extend our deepest sympathies to the Casey family."
In a statement Tyrone GAA said they were "totally shaken" by the news, describing Mr Casey as "a supreme hurler... at the peak of his powers".
Tyrone county chair Michael Kerr said he brought "honour, delight and gladness to the whole county and far beyond".
"There are very difficult days ahead for Sean, Susan, Louise and Catherine, for Damian's wider family circle and many friends and associates, for his team-mates and for the Gaels of Dungannon and Tyrone," he added.
"Our deepest sympathy goes to them, and our focus must now be on providing the support and comfort that will be so badly needed".
By BBC Sport NI's Mark Sidebottom
Damian Casey was the heartbeat of Tyrone hurling for the last decade.
After making his inter-county debut in 2012, he went on to play more than 100 consecutive league and championship games and is by some stretch, the county's most prolific scorer of all time.
Uniquely, Damian Casey scored in every game of hurling he played for Tyrone.
His career tally of 39 goals and 906 points is never likely to be surpassed.
Sinn Féin MP Michelle Gildernew said the community in Dungannon was heartbroken by the news.
She said Mr Casey was "possibly the best hurler ever in Tyrone".
"His death is devastating for the county, but unimaginable for Sean, Susan, Louise and Catherine," she added.
The news of Mr Casey's death prompted tributes from the GAA community via Twitter.
Ulster University Gaelic Academy said: "We are profoundly saddened to learn of the tragic death of Damian, esteemed graduate of UU and Fitzgibbon hurler.
"We extend our deepest sympathy and offer our sincere condolences to the entire family circle at this very sad time."
The Gaelic Players Association said: "Players across Ireland are devastated for the family and friends of Damian Casey and for all in Eoghan Ruadh and Tyrone GAA.
"Damian stood out as a person and leader. On the pitch he was a magician of rare skill.
"He was one of us. He was among the best of us."
Coalisland Clonoe CCE tweeted: "Sincere condolences to Damian Casey's family, friends and Club.
"We feel your loss and heartbreak.
"Ar dheis Dé go raibh a anam".
Strabane Sigersons GAA said: "RIP Damian Casey.
"Once again people awaken in Tyrone GAA circles to heartbreaking news.
"No words are enough to pay tribute to an outstanding gael like Damian.
"Our thoughts and prayers are with his friends and family".
Seán Ó Treasaigh hurling club also paid tribute: "All at Sean Treacys Lurgan would like to pass on our heartfelt condolences to Eoghan Ruadh and Tyrone GAA and the family friends and team mates of Damian Casey after his tragic passing.
"Ulster hurling has lost an absolute great. Rest Easy Damian."