The 13-month-old girl died of head injuries in King's College Hospital, south London, on Saturday, 4 December.
The child, from Peckham, south London, was brought in 10 hours earlier at 1.30am.
Scotland Yard said her death had been caused by a brain haemorrhage and was being treated as murder. 'We can confirm a nine-year-old boy, not related to the deceased, has been spoken to by police in the presence of a responsible adult,' a spokeswoman said.
Children of nine are below the age of criminal responsibility and cannot be charged with murder or any other criminal offence.
An inquest into the girl's death was opened and adjourned by the Inner South London coroner last week.