A medical investigation has been launched at Cork University Maternity Hospital (CUMH).
The mother of a newborn child was found dead on the floor of her room on Monday.
The infant was reportedly found seriously injured beside her mother.
However, the child is now said to be in a serious but stable condition.
One possibility being investigated is that the woman may have become unwell, and fell out of bed while breastfeeding.
A spokesperson for the South South West Hospital Group expressed its "deepest sympathy with the family of the patient who died".
Thy added: "The priority for the hospital is the well-being of the patient's child and the wider family."
The hospital said a full medical investigation was immediately initiated, as is the case with all maternal deaths.
"This investigation is currently underway at CUMH", it added.