The Ambulance Service received a 999 call following what has been described as an incident at a private address in the town.
A spokesperson for the Northern Ireland Ambulance Service added: "We received a 999 call at 11:12am following a medical incident at a private address in the Kennedy Square area of Downpatrick.
"NIAS dispatched two Emergency Crews, two Officers and the Charity Air Ambulance with HEMS on board were also in attendance.”
SDLP Councillor Dermot Curran said: "I want to offer my condolences to the family involved. And if there is anything I can do to help I am willing to do it at this time."