All water dispensers at the facility were taken out of action last Friday after the bug was discovered during routine water testing.
A spokesperson for the Western Health and Social Care Trust said they will not be put back in use until a full review is complete.
"Water dispensers are located within ward pantries, patient sitting and visitor waiting areas of the South West Acute Hospital," the trust said.
"As part of Northern Ireland Health Group's routine water testing, they have identified some dispensers where pseudomonas has been detected."
The trust said the discovery is isolated to the water dispensers themselves.
It continued: "The public can be assured that this is not an issue with the water quality of the main water supply at the hospital but is an isolated issue with the water dispensers themselves and has had no impact on patient care."
Four babies died from pseudomonas in NI hospitals in December 2011 and January 2012.
The first death happened at Altnagelvin Hospital in Co Londonderry then three more babies died from a different strain at Belfast's Royal Jubilee Maternity Unit the following month.
Police launched an investigation into the deaths.
The state-of-the-art new South West Acute Hospital replaced the Erne Hospital when it opened in Enniskillen in June 2012.