A Hato Hone St John spokesperson said they were notified of the incident, in Russell St, at 11.57am.
An ambulance and an operations manager responded.
A patient was transported to Dunedin Hospital in a moderate condition, the spokesperson said.
Two fire appliances and firefighters were seen in the street.
A Fire and Emergency New Zealand (Fenz) station officer at the scene said a heater had "fallen off the wall" on to an elderly man inside an address. He had needed assistance getting out.
A Fenz spokesman said crews responded from Willowbank and Dunedin.
The man was no longer trapped when they arrived, but they assisted with "extricating" the patient to the ambulance.