A Brisbane woman accused of allowing her baby girl to become malnourished and using the child's story to establish a GoFundMe page that raised more than $15,000 has been granted bail.

The 27-year-old woman, who cannot be identified for legal reasons, was arrested on Thursday after a long police investigation, and charged with torture, grievous bodily harm and fraud.

Police said they were first notified about the case in July, by which point the woman's 10-month-old baby girl had been treated in hospital a number of times with signs of malnourishment.

It was alleged the mother set up a fundraising site using her baby's condition to raise money to support her family.

The GoFundMe page set up in February has raised more than $15,000.

She appeared in the Brisbane Magistrates Court this morning where she was granted bail, subject to a number of conditions including she have no unsupervised contact with the infant.

She is due to reappear in court on December 12.

ABC/AAP