Begum surfaced in a Syrian refugee camp following her escape from the collapsing ISIS "caliphate" and has pleaded to be allowed to return.
The BBC reported that a medical certificate indicated that pneumonia was the cause of death.
When Begum first started speaking to reporters more than three weeks ago, she said the first two children she had given birth to since joining the extremist group had died of malnutrition and other ailments.
After Begum was stripped of her citizenship, her family tried to challenge the decision and asked for help in bringing her baby back to the UK. Zara, 28, already had a son when she made the journey and was heavily pregnant with her second child, to whom she gave birth in Syria.
The lawyer for the family of Shamima Begum, Mohammed T Akunjee, said: "I can confirm that it is our understanding that Shamima has been moved from Al-Hol due to safety concerns around her and her baby. I am willing to change", she said, following the revocation of her citizenship.
Begum is now believed to be in a refugee camp closer to the Iraqi border after being removed from the Al-Hol camp in the north of Syria due to alleged threats following the worldwide media attention she attracted.
Camera IconCCTV of Shamima Begum leaving at Gatwick Airport
It instructed Begum's sister to make her pleas to the Foreign and Commonwealth Office "which is obliged to consider request for consular assistance".
"Clearly Shamima Begum holds abhorrent views, Phillip Lee, former justice minister and member of Theresa May's party told BBC radio".
Last month he told British lawmakers: "Children should not suffer, so if a parent does lose their British citizenship it does not affect the rights of their child". The foreign secretary has said it was too risky to send British officials to rescue Shamima Begum's baby son from Syria, and said the lack of access to medical facilities was a result of Begum leaving British soil to go and live under the ISIS.
Shamima Begum's new born son has died in a displaced people's camp in northern Syria. "This is a reminder of why it is so, so unsafe for anyone to be in this war zone". "This is callous and inhumane".
Jeremy Hunt revealed officials are working to rescue children born to rescue British children born to women who joined ISIS.
"The security services came to speak to me and I was honest", she told the newspaper.
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