It is understood that the woman's car was parked at the rear of the property when a section of the garden collapsed under it, causing it to partially fall into a sinkhole.
Emergency services were called to the woman's house on Caemawr Road in Morriston yesterday at 8.55am to help her; she was then taken to hospital, where she is said to be in a "critical" condition.
A police spokesman said to the South Wales Evening Post: “Emergency services were called to Caemawr Road in Morriston on Wednesday morning following reports that a woman had suffered injuries after being involved in an incident involving a car at the rear of a house.
“The woman, who is in her 50s, has been taken to Morriston Hospital with serious injuries.
“An investigation to establish what happened is underway.”