The teenager and her infant son were moved from the Al-Hol camp in the north of the country due to “safety concerns around her and her baby”, Tasnime Akunjee said.
Ms Begum, who fled from Bethnal Green in east London to join Islamic State as a 15-year-old, recently said she regretted speaking to the media.
The 19-year-old, who gave birth days after her discovery by a journalist was first reported, said she wished she had kept a low profile.
The Sun reported that Ms Begum, who wants to return to the UK but has been stripped of her British citizenship, had received death threats since speaking out about her plight.
The mother and her baby are said to have since been moved to another camp nearer to the Iraqi border.
Mr Akunjee told the paper: “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.
“We further understand that indeed she and her child had been threatened by others at the Al-Hol camp.”
The development comes after British officials ruled out any effort inside Syria to extract Ms Begum and her child.
Home Secretary Sajid Javid stripped her of her British citizenship in an effort to block her return.
Ms Begum’s family have pleaded for the mother and her child to be allowed to come back to Britain.
They say the teenager should face justice if she is found to have broken the law by travelling to Syria.