Police were called to a house on Gregg House Road, Shiregreen, near Hartley Brook Primary School at around 7.30am this morning.
Yorkshire Ambulance Service and Yorkshire Air Ambulance were called to the scene and took six children to hospital.
One eyewitness said: "I saw a man and a woman coming out of the house in handcuffs and taken away in a police car.
"There was a police officer cradling a baby outside the house – the baby seemed to be okay."
A huge police cordon remains in place at the scene and police officers are continuing their enquiries.
South Yorkshire Police said two people were under arrest but did not disclose any further details.
The incident happened around 50 yards from Hartley Brook Primary School.
A spokeswoman for the school said: "There was nothing at all that's happened at the school.
"The kids are in school as normal. We are not under lockdown."
Anyone with any information should call police on 101.