British-born teenager Shamima Begum was recently stripped of her citizenship for joining the IS.
And the 19-year-old gave birth last month in a refugee camp in northeast Syria
Syrian Democratic Forces (SDF) spokesman Mustefa Bali confirmed to AFP that the baby had since died, but declined to specify how or when it happened.
He had previously denied the baby had died in a Twitter post that has since been deleted.
Ms Begum travelled from east London to Syria in 2015 and said she had previously given birth to two other children.
They are said to have also died, apparently from illness and malnutrition.
Britain stripped Begum of her citizenship last month despite her wishes to return to the country, although the government hinted her newborn son could be treated differently.
Renu, eldest sister of Shamima Begum holds her sister's photo whilst being interviewed by the media at New Scotland Yard, Central London. Source: Press Association
Save the Children has said the death could have been avoided. It said more than 60 children under the age of five have died en route or on arrival at he camps.
"We know that conditions are increasingly desperate in the displacement camps as thousands of people arrive every day from the remaining ISIS-held areas, many of them sick and malnourished young children," the charity said in a statement.
"All children associated with ISIS are victims of the conflict and must be treated as such. The death of each child is an unacceptable tragedy.
"The UK and other countries of origin must take responsibility for their citizens inside North East Syria."
A mass exodus from the jihadists' last redoubt in eastern Syria has sparked a humanitarian emergency, as the SDF leads an offensive to smash the last remnants of the IS "caliphate".
The International Rescue Committee on Friday said that 12,000 women and children had arrived at the Kurdish-run Al-Hol camp since Wednesday.
Since December at least 100 people have died en route to the camp or shortly after arriving, mostly children under five, the IRC said.
Ms Begum was 15 when she caught a flight in 2015 to join IS. Source: AAP
