Permissibility of Transferring the Child from His Mother’s Custody When There Is Fear for Him]

Answer—and Allah grants success: If there is fear that tuberculosis will affect the child’s health, it is permissible for his guardian to remove him from his mother—or his grandmother, maternal aunt, and the like—and custody transfers to the next entitled custodian after her. Whether tuberculosis and similar illnesses are contagious or not is determined by physicians; if the illness is not contagious, custody is not voided by it.
In sum: a child’s custody turns upon what is best for the child. The mother is more entitled to her child than others, for she is gentler with him and more compassionate toward him. But if there is fear of the child’s contracting tuberculosis—as in the question—or something similar, then in that case someone other than her is better for the child.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1