The police were called to a property in Nightingale Avenue, Castle Bromwich in the West Midlands last Wednesday after receiving reports that a child had collapsed.
ITV news claims paramedics at the scene attempted to treat the little boy, but were unable to save his life and he later died in hospital.
The couple, a female of 25, and male of 29, were originally detained on Wednesday on suspicion of willful neglect. They were then arrested on Friday on suspicion of murder.
The child's identity has not been released by the police, and a spokesperson told the BBC that post-mortem results could take 'some time'.
The man and woman have been released on police bail.