Police were called by the London Ambulance Service to an address in Lansdowne Crescent shortly after 2.25pm on Monday October 29 following reports of an injured infant.
On arrival, officers found a two-year-old girl who was treated by paramedics and taken to a west London hospital. She was pronounced dead at 3.17pm.
A post-mortem at Great Ormond Street Hospital is scheduled to take place in due course.
The spokesman said a woman, believed to be the toddler's mother, was taken to hospital and treated for shock.
Officers from Kensington and Chelsea CID are investigating the incident. At this stage it is being treated as non-suspicious.
More top news
London Ambulance Service has more paramedic job vacancies than anywhere else in England.
Hundreds of people march for more affordable homes and control private rents in London.
Police proposals suggest that all frontline police officers should have the option of arming themselves with Tasers.