Officers were called to the address in Clifton at around 1.25am today.
One man, who was in the house at the time, suffered serious injuries, although they are not believed to be life threatening.
Fire and ambulance crews were also called to the address, in Morehall Close.
A man in his 20s, believed to be the driver of the car, has been arrested in connection with the incident.
He sustained minor injuries in the collision and was taken to hospital. The two other people were in the car at the time also received medical attention.
A woman who was in the house was uninjured.
The car, a white Volkswagen Golf R, is being recovered from the living room area of the house following a structural assessment of the property.
Police are appealing for witnesses and anyone who saw the car in the moments leading up to the collision as it travelled along Longwood Road/Rivelin Way, or elsewhere in the Clifton area.
If you have any information that could help police, call 101, select option 2 and ask for Hamish Halloway.
You can also email Traffic Sergeant Halloway at Hamish.Halloway@northyorkshire.pnn.police.uk
Please quote incident number 12170157578 when sharing information.