Police were called to a address in Bradford, West Yorks, at about 5.10pm on Saturday following a report that the baby boy had suffered life-threatening injuries.
Det Supt Nick Wallen said: “This is clearly an extremely traumatic incident and specially trained officers are working to support the child’s family members and those who witnessed the incident.
“Those who witnessed this incident will have been deeply traumatised by what they saw”
Det Supt Nick Wallen
“It is no exaggeration to say those who witnessed this incident will have been deeply traumatised by what they saw.
“A 23-year-old woman has been arrested on suspicion of murder in connection with the baby’s fall and she is currently receiving medical assessment in custody.”
Police said they are not looking for anyone else in connection with the incident but have appealed for witnesses or anyone with information to come forward.
Police said the baby died after falling from a top-floor flat at Newcastle House in Bradford
A crime scene remains in place at the scene as inquiries continue.
Anyone with any information is asked to contact Bradford CID on 101, quoting reference number 1506 of October 21 2017.