Police and paramedics were called to an address in Blossomville Way, in Acocks Green, at 7.25am on Thursday, following reports a child was unconscious at the address.
The boy was taken to hospital but was pronounced dead at 8.20am.
A 44-year-old woman from Acocks Green has been arrested on suspicion of child neglect and remains in police custody, the force said.
Detectives are treating the death as unexplained and a post-mortem examination is due to take place.
A West Midlands Ambulance Service spokesman said earlier: "We were called to reports of a medical emergency at a property on Blossomville Way at 7.19am this morning.
"Two ambulances, a paramedic officer and the Midlands Air Ambulance Critical Care Car were sent to the scene.
"On arrival we discovered one patient, a boy, who was in a critical condition.
"He received specialist trauma care at the scene before being transported to Heartlands Hospital.
"Sadly, it later became apparent at hospital that nothing could be done to save him and he was confirmed deceased."
Detective Inspector Joe Davenport said: "This is a truly tragic incident in which a young boy has been found dead.
"We understand he had some underlying health issues and was admitted to hospital recently.
"We've launched an inquiry to understand what happened in the days leading up to his death and to determine if any factors have contributed to his death."