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
Police are attempting to find a vulnerable missing 16-year-old girl who is feared to be with a 51-year-old man.
The owners of two Hackney bakeries have had to pay £28,000 after infestations of cockroaches and mice were found on the premises.
After failing to get his hands on any tickets for Arsenal fans for the FA Cup final, one unlucky supporter appealed for Royal assistance.