Hayley Davidson had been at the Royal Hospital for Sick Children in Edinburgh since police were called to a flat in West High Street, Buckhaven, on Sunday.
A statement from the baby's family said Hayley was "a beautiful baby girl who was loved by everyone who met her".
Police Scotland said: "A thorough and rigourous investigation is ongoing as officers progress with inquiries."
Chf Insp Adrian Annandale added: "This is an extremely tragic and sensitive case and I'd like to reassure Hayley's family as well as the wider community that we're conducting a robust investigation and appreciate the assistance provided."
A five-month-old baby girl found in a critical condition after an incident at a Fife flat has died.