BBC Jersey's Tim Pryor says police are at the scene, where an area has been cordoned off.
States of Jersey Police head of crime services Stewart Gull, who is leading the inquiry, said: "Clearly this complex investigation is in its very early stages as we try to establish exactly what happened.
"We are appealing to anyone who may have any information to contact us.
"We are mindful, too, of the impact of any such serious and tragic incident on the local community, and we have police officers in the area to support the investigation and local people."
A major incident room has been set up at and police are appealing for anyone with information to contact them.
Eyewitness Andre Thorpe said he believed all the victims were members of the same family and it appeared a child was among them.
Mr Thorpe said: "For Jersey it was a major incident. Two ambulances turned up first because it was within a quarter of mile of the ambulance station.
"Then four or five police vehicles came, all blues and twos.
"They were trying to access a private house in the crescent. It was an old Victorian terrace, a lot of them are split into flats."
Mr Thorpe added that the area where the incident happened was quite secluded and not on a main road.
"I was first aware something was happening when I saw people looking out for the ambulances as I walked up the road," he said.
Police urged anyone with information to contact them on 01534 612612.