Officers were called to Helliers Road in Chard, Somerset, at about 23:30 BST on 16 July.
The injured child was taken to hospital and died on 23 July, police said.
A 35-year-old man was arrested on suspicion of causing grievous bodily harm with intent and was released on bail. A 24-year-old woman was arrested then released under investigation.
Det Ch Insp Simon Dewfall from Avon and Somerset Police said: “We’re carrying out a full and thorough investigation into this tragic incident, which will seek to determine how and why this baby has suffered these injuries.
“Specialist liaison officers are supporting the baby’s family during this incredibly difficult time.
“While we’re treating this as an isolated incident, we know this will be of significant concern to the local community.”
Source: BBC