Police were called to Dovey Road in Sparkhill just after 3.40am
The baby was not breathing.
He was taken to hospital by paramedics but pronounced dead a short time later.
A man aged 29 was arrested at the scene on suspicion of murder.
A woman aged 26 suffered injuries which are not believed to be life threatening in the same incident and was taken to hospital for treatment.
A second woman was taken to hospital to be treated for a head injury, and has since been discharged.
Detectives are not looking for anyone else in connection with the investigation.
Insp Neil Kirkpatrick, in charge of policing in the area, said: “This is a real tragedy and our thoughts go out to everyone involved.
“We’ll have extra officers in the area over the coming days to offer reassurance.”
