Published Friday, 03 February 2012
It happened in a salon above a shop on Carland Road, opposite the South Tyrone Hospital, at around 4.15pm on Friday.
The man is believed to be from the Brantry area a few miles outside the town.
A statement from the PSNI said: "Police are investigating the circumstances of the incident but are not looking for anyone else in connection to this death."
Officers said it is not believed a crime has been committed.
Local MLA Maurice Morrow described the death as a "very sad and tragic incident" that has left the town in shock.
"There's obviously a family in sorrow and in grief here tonight in the Dungannon area," the DUP representative told UTV.
"My heart goes out to the family that are involved and I just want them to know that our thoughts are with them at this particularly difficult time.
"I understand that a young man has taken his own life and from speaking to the police they are not looking for anyone else and it is a real, real tragedy for this family and for other families and indeed for the whole of Dungannon."
The name of the young man has not yet been released.