South Yorkshire Police said the teenagers, aged 13 and 14, died after they were taken to hospital yesterday morning.
Four other children aged 11, 10 and three and one other aged seven months remain in hospital receiving treatment but they are not in a life-threatening condition, a spokesman said.
The children cannot be named for legal reasons.
The force said officers were called to the semi-detached house in Gregg House Road in the Shiregreen area of the city at about 7:30am.
But detectives have given no indication about the nature of the incident apart from confirming it was not a shooting and that it was confined to the one property.
A 37-year-old man and a 34-year-old woman have been arrested on suspicion of murder in connection with the incident, police said.
A spokesman said detectives are not looking for anyone else in connection with the incident. Speaking at the scene, Superintendent Paul McCurry said: “I think it’s really important that I reassure the wider community that there’s no wider risk.”
Mr McCurry said: “The investigation is at a very early stage and detectives are working closely with a number of different lines of inquiry.
“Our detectives are supporting the family.”
The senior officer said: “I’m aware of wider speculation regarding the use of weapons. At the moment there is no wider risk to the community in Sheffield.”
He said the children in hospital are conscious, and added: “They are being given the necessary care that they need. And they will be in hospital for certainly the next few hours.”
He said a post-mortem examination would take place later.
Mr McCurry said officers were alerted after an “independent call for assistance”.
People living nearby said they were shocked to see more than a dozen police cars and four ambulances arrive on the tree-lined road and an air ambulance land in the grounds of Hartley Brook Primary Academy, which is just 100 metres from the scene.
Detective Chief Inspector Simon Palmer, who is leading the investigation, said: “To allow the investigation to progress, I would please ask that people are mindful of what they are posting on social media, and the potential distress this may cause.”
The street was partially cordoned off as police officers and forensics teams examined the council-style property where the incident happened.
The three-bedroom property is similar to many on the north Sheffield estate, but has an unkempt garden with an old, yellow Ford Fiesta parked on the front lawn, apparently abandoned.