The bacterial bug, called Pseudomonas, killed three babies when it was discovered in a hospital in Northern Ireland.
Doctors at the Norfolk and Norwich University Hospital say it's been caught early here.
No babies in Norwich have been infected with the disease and the hospital says its taking extra safety precautions.
Pseudomonas can be found in soil, taps and sinks. It's able to live on surfaces for several hours and can be passed from person to person. Most healthy people are not at risk but it can cause serious infections in people with weak immune systems. It's hard to treat as it's resistant to many antibiotics.
The hospital says as a precautionary measure it is using sterile water instead to protect babies in the unit.