Renu Begum claimed her sibling had been lost to a “murderous and misogynistic cult” after fleeing London to join the terrorist group in Syria as a schoolgirl in 2015.
But in a powerful message to Home Secretary Mr Javid, she said the family “cannot simply abandon her” and said they would challenge a move to revoke her UK citizenship.
"Firstly, we wish to make clear, that along with the rest of the country, we are shocked and appalled at the vile comments she has made to the media in recent days," the letter read.
Ms Begum, now 19, is living in a refugee camp in northern Syria along with her newborn son and said she wants to return to Britain.
The letter, seen by the BBC, said the baby boy was a "true innocent" who should not "lose the privilege of being raised in the safety of this country".
It added: "We request that your office contacts our solicitor... to discuss the practical mechanics of how to help my nephew find his way home."
The family said they have had no contact with Ms Begum and had only learned she had given birth to a boy through media reports.
Ms Begum was one of three schoolgirls to leave Bethnal Green to join the terror cult in 2015 and resurfaced heavily pregnant at a Syrian refugee camp last week.
Her family's letter said they had made "every fathomable effort" to block her from entering IS territory.
"That year we lost Shamima to a murderous and misogynistic cult," her sister wrote. "My sister has been in their thrall now for four years, and it is clear to me that her exploitation at their hands has fundamentally damaged her."
The Home Secretary revoked Ms Begum's British citizenship in a move only permissible under international law if it does not leave the individual stateless.
It was speculated that Ms Begum, who is of Bangladeshi heritage, may have citizenship there but Bangladesh's minister of state for foreign affairs Shahriar Alam denied this.
BBC EXCLUSIVE: Renu Begum is sending this letter to the Home Secretary. She is telling him they are challenging his decision to take away Shamima Begum's citizenship, and she is asking him to help bring her nephew Jarrar home https://t.co/8lRoRJHmGa pic.twitter.com/5HmRY2PaRA
— Daniel Sandford (@BBCDanielS)
Appealing to the home secretary, the family said: "We are sickened by the comments she has made, but, as a family man yourself, we hope you will understand that we, as her family cannot simply abandon her.
"We hope you understand our position in this respect and why we must, therefore, assist Shamima in challenging your decision to take away the one thing that is her only hope at rehabilitation, her British citizenship.
"Shamima's status will now be a matter for our British courts to decide in due course."
Ms Begum earlier told Sky News she had no desire to go to Bangladesh: "I don't have anything there, another language, I have never even seen the place."
Mr Javid's removal of her citizenship came amid heated debate over whether the teenager should be able to return to the UK after she was found in a Syrian refugee camp with the terror group's reign nearly over.
The Muslim Council of Britain has warned Mr Javid's move heightens fears of "a two-tiered citizenship scheme, sets a dangerous precedent and demonstrates an abdication of responsibility".
While many do not want to see Ms Begum return to the UK, others have argued she should face prosecution for her actions, and attempts at deradicalisation.
The Begum family's lawyer Tasnime Akunjee said she was born in the UK, has never had a Bangladeshi passport and is not a dual citizen, which was confirmed by the Bangladeshi minister.
Mr Alam added: "So, there is no question of her being allowed to enter into Bangladesh."
Asked about the situation on ITV's Peston, Mr Javid said: "I'm not going to talk about an individual, but I can be clear on the point that I would not take a decision and I believe none of my predecessors ever have taken a decision that at the point the decision is taken would leave that individual stateless."
He also suggested to the Commons that action to bar her from returning will not impact her son's rights.
"If a parent does lose their British citizenship, it does not affect the rights of their child," he said.
The British Nationality Act 1981 provides the Home Secretary with the power to strip people of citizenship if it is "conducive to the public good".
Meanwhile, the Government's chief adviser on countering extremism warned radical Islamists could exploit the unease caused by Mr Javid's move.
Independent adviser Sara Khan said: "The Government has to recognise the unease felt by a wide range of people about decisions of this kind, not least those from minority communities with dual nationality.
"It has to build trust in its approach, because Islamist extremists will exploit alienation and grievance to turn people against their country."