Staff at the Queen's Medical Centre (QMC) in Nottingham said they could do no more for Indi Gregory, who has mitochondrial disease.
Christian Concern, which has been supporting her parents, said the eight-month-old had been moved to a hospice.
It comes after the Derbyshire family'sappeal to take her homewas rejected.
In a statement issued through the group, Indi's father said she was "fighting hard".
Dean Gregory and Claire Staniforth, from Ilkeston, wanted specialists to keep treating their daughter but the couple lost fights in both the High Court and Court of Appeal.
A spokesman for Christian Concern said Indi's life support had now been withdrawn and she had been moved to a hospice.
High Court judge Mr Justice Peel ruled limiting treatment would be lawful, and doing so would be in Indi's best interests.
Her parents failed to persuade Court of Appeal judges and judges at the European Court of Human Rights, to overturn the decision.
The couple also failed in a bid to transfer Indi to ahospital in Rome.
It was ruled a move to Italy would not be in Indi's best interests and Court of Appeal judges backed the decision.
Judges heard Indi has mitochondrial disease - a genetic condition that saps energy.
Specialists said she was dying and the treatment she was receiving caused pain and was futile but her parents disagreed.
Mr Justice Peel considered evidence at private hearings in the Family Division of the High Court in London.
Specialists have withdrawn life-support treatment from a critically ill baby girl who has been at the centre of a legal battle.