Detectives from Hampshire Police charged the teenager on Tuesday night after he was arrested that morning.
He is due to appear at Southampton Magistrates' Court on Wednesday.
The arrest came after officers and paramedics were called to Defender Road at 5.05am on Sunday, following reports that a child was in need of medical attention.
The baby boy was taken to Southampton General Hospital, where he later died.
An 18-year-old woman was also arrested on suspicion of murder and remains under investigation, but has been released from police custody.