It is understood the 13-month-old girl from the Lithuanian community had been living in the Enniskillen area.
The PHA has confirmed the young child died after taking ill with meningococcal septicaemia but stressed that any risk to other people was very small.
It is believed the baby girl fell ill on Friday, November 9 and died that weekend.
A consultant has reassured the local community that the risk of infection to other people was extremely low.
Extending her sympathies to the family, Dr Anne Wilson, Consultant in Health Protection for the PHA, said: "Antibiotics are offered only to those people who have had close and prolonged personal contact with the patient. National guidance on this matter is that antibiotics are not widely offered as a preventative measure as they can clear protective organisms from the throat, and as a consequence can increase rather than reduce the risk of infection,"
According to Dr Wilson, the PHA had taken "well-established steps" to minimise the risk of infection to others by offering antibiotics to those who had recent prolonged personal contact with the child.
"The risk of other people contracting this type of infection is negligible, so there is no cause for concern among the wider community; however it is important to be aware of the signs and symptoms of meningitis," she said, "These may include severe headache, dislike of bright lights, vomiting, neck stiffness, non-blanching rash and drowsiness. Should anyone develop any of these they should contact their GP or local A&E department immediately," she added.
Further information on meningococcal septicaemia can be found on the Health Protection Agency website http://www.hpa.org.uk/Topics/InfectiousDiseases/InfectionsAZ/MeningococcalDisease/.