Emergency services were called to the property in the Cyncoed area of the city just after 09:30 BST on Thursday.
Council workers are assessing the house to see if it is safe for the BMW 4x4 to be removed, while the owners of the property have been evacuated.
An ambulance service spokesman said a man was given a precautionary check-up at the scene but did not require hospital treatment.
The occupants of the house have been evacuated while building inspectors from the council survey the house for damage.
A car has gone through a garden wall and into a house in Cardiff.