The property in Creigiau, which was under construction, was ravaged by fire on Thursday night.
South Wales Fire and Rescue Service was called at about 21:15 BST but no-one was injured in the blaze.
On Friday, the fire service's head of control, Jennie Griffiths, tweeted that the fire was started deliberately and the house "suffered partial collapse".
Fire crews will revisit the site on Friday to check it.
A house in Cardiff has partially collapsed after an arson attack.