Begum, whose first two children also died, was stripped of her British citizenship last month on security grounds after she was discovered in a detention camp in Syria.
The 19-year-old left London to join IS when she was 15. She had sought to return to Europe with her third child, who was born about three weeks ago.
SDF spokesman Mustafa Bali said the child had died. Begum has said in media interviews her son was named Jarrah.
A British government spokesman said: “The death of any child is tragic and deeply distressing for the family.
The fate of Begum has illustrated the ethical, legal and security conundrum that governments face when dealing with the families of militants who swore to destroy the West.
(Production: Soraya Ali)