All babies in the unit were tested after "higher than normal" levels of the bacteria were found in the water system. None has been found to have developed clinical signs of infection.
In Northern Ireland, four babies have died since December after developing Pseudomonas infections.
The first died that month after contracting the bug at the Altnagelvin Hospital in Londonderry, while the other three died in January after catching a different strain at the Royal Jubillee Maternity Hospital in Belfast.
Dr David Booth, a consultant in the Norwich unit, said: "The safety of the babies in our care and supporting their parents and families are our priorities.
"We would like to emphasise that none of our babies are showing any signs of Pseudomonal infection."
A spokesman said staff had met individually with parents of all babies in the unit, which remains open.
She added: "As a precautionary measure we are using sterile water instead to protect babies in the unit."
She pointed out that there might be no link between the contaminated water and the bacteria found on the babies' skin. Samples are currently being analysed to help determine the source of the outbreak.
Pseudomonas aeruginosa, to give the bacterium its full name, is commonly found in the environment, for example in stagnant water, soil and on people's skin. Usually it causes no problems.
However, it can pose a threat to people with weak immune systems, such as the elderly, sick, or very young babies.
The Health Protection Agency has warned that it is "increasingly important clinically as it is a major cause of both healthcare-associated infections and chronic lung infections in people with cystic fibrosis".
It is "one of the more common causes of healthcare-associated infections and is increasingly resistant to many antibiotics".
The bacterium is hardy and can survive for many days on surfaces, meaning it is a priority for hospital infection control managers.
Between 2006 and 2010 the number of infections in England, Wales and Northern Ireland has fluctuated between around 3,700 and 4,000. They are most frequent in those aged 65 or older, and babies under a year.
The Northern Ireland spate of deaths led to a deep clean of all the region's neo-natal unit, including replacing their 175 taps. A number of contaminated water taps are thought to have been the source.
A full investigation by the Regulation and Quality Improvement Authority (RQIA), the independent health and social care regulatory body for Northern Ireland, is now underway.
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