The child was taken to hospital where she was pronounced dead.
A 27-year-old woman was arrested at the hospital and a 52-year-old man was detained at an address in east London later on Wednesday.
The pair are being held in custody at separate police stations.
The girl has not been formally identified and a post-mortem examination will take place on Friday.
Detective Chief Inspector Gary Holmes said: “The death of any child is tragic and we would appeal for anyone with information to please come forward as soon as possible to help with our inquiries.”
Anyone with information is asked to call police on 020 8345 1570 or Crimestoppers on 0800 555 111.