The boy was taken from a home in Velville Court in Newcastle to hospital with serious injuries, on Friday.
A 34-year-old man and a woman, aged 30, are currently in police custody and are due to be questioned.
Northumbria Police said the baby died on Monday and officers are treating the injuries he had suffered were "non-accidental".
Det Ch Insp Mark Ord said: "We are treating the death as a homicide investigation.
"We know this will shock and sadden the local community and I would like to reassure them we are doing everything we can to establish exactly what happened and how the baby came to suffer such fatal injuries.
"This is a very tragic incident and our thoughts are with all those affected by this sad death."
Two people have been arrested on suspicion of murder after a 13-week-old baby died.