A man has been arrested on suspicion of murder following the incident at a house in Kent Road on Friday.
Officers were called shortly before 1am after a neighbour heard a disturbance and found the girl with multiple injuries, including one to the head.
The 51-year-old suspect, who is related to the girl, is also in hospital receiving treatment for a cut hand.
A woman in her 80s suffered a suspected dislocated shoulder during the incident.
Superintendent Harvi Khatkar said: "This is an extremely distressing incident and our sympathies go out to everyone affected.
"We are working to establish exactly what has happened, and fully understand the impact that this will have on the community.
"But we do believe this is an isolated incident, and we are not looking for anyone else.
"Extra officers will be out patrolling the area to offer reassurance to residents."
The house has been cordoned off to allow forensic experts to conduct an examination.
A post-mortem examination is expected to take place on Sunday.
West Midlands Police are not looking for anyone else in connection with the incident.
One neighbour, who knew of the schoolgirl, described her as "always smiling".
Anyone with information can call police on 101, quoting log 77 of 9 February.