A Bench headed by Chief Justice Ranjan Gogoi made the order after the Uttar Pradesh government raised no objection on a plea seeking his transfer to the Tihar Jail.
The uncle is serving 10 year jail term in Uttar Pradesh.
Meanwhile, the court directed the media not to disclose the identity of the victim after it was informed that some old videos of the girl and her family had been made public.
On July 28, the rape victim was travelling to Rae Bareli with her lawyer Mahendra Singh and two aunts when a truck being driven on the wrong side hit them.
The rape victim and her lawyer are on life support. Of the two aunts killed in the accident, one was a witness to the crime.
The relatives of the rape victim and the lawyer informed the Supreme Court on Friday that their treatment can continue at the King George Medical College in Lucknow.
The Supreme Court had offered to airlift them to the All India Institute of Medical Sciences in New Delhi.
The Bench nominated Justice Deepak Gupta to hear the Unnao case in which the girl has accused the now sacked BJP MLA Kuldeep Singh Sengar of raping her in 2007.
The court was informed that the UP government has paid the compensation ordered by the apex court to the victim and that the CRPF had taken over the security of the victim and lawyer since Thursday night.
The next date of hearing is Monday.
Chief Justice Gogoi on Wednesday took suo moto cognisance of a letter written by the family of the victim alleging threats from Sengar's men.
( With inputs from IANS )