A Brisbane children's hospital is refusing to release a baby being treated for burns suffered while in detention on Nauru until a "suitable" home is found.

The 12-month-old's wounds have healed and she's in a stable condition. However, medical staff won't discharge the girl who's being treated at Lady Cilento Children's Hospital.

"This patient will only be discharged once a suitable home environment is identified," a hospital spokesman said in a statement.

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The spokesman said it was up to qualified clinical staff to decide when a patient should be discharged.

It's understood the girl is a baby known as Asha who in mid-2015 became the first infant born into detention in Australia to be transferred to Nauru.

The baby suffered the burns when boiling water was accidentally spilt on her on Nauru and she was transferred to Lady Cilento at the end of last month.

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Her mother is by her side and the girl's father is being detained at Pinkenba, north of Brisbane, but has been visiting the hospital.