The Department of the Environment (DoE) said it had been five years since the first recorded death due to the virus in Northern Ireland.
The Northern Ireland Environment Agency (NIEA) said there appeared to be "little natural resistance to the virus within the local population".
It said sick squirrels tend to die within 10 days to two weeks.
NIEA Wildlife Inspector Declan Looney said red squirrels in Tollymore Forest had "recovered well" following the outbreak of the virus five years ago, but this was a "further blow".
"Sick red squirrels will appear lethargic, approachable, with painful sores on their faces and paws," he said.
"Unfortunately there appears little natural resistance to the virus within the local population and sick animals tend to die within 10 days to two weeks.
"If you have squirrels entering your garden to feed at bird feeders, please either remove these or clean them daily to reduce the spread of the virus."
The DoE said the disease "does not affect people or their domestic pets".
A spokesperson from the Forest Service said it was "not unusual" for the virus "to re-emerge some years after the initial outbreak".
"The fact that the red squirrel population recovered in the intervening years gives us great encouragement that working in partnership with the NIEA and the Tollymore Red Squirrel Group on the implementation of control measures will once again produce a successful outcome," they added.
There has been a squirrel pox virus outbreak among red squirrels at Tollymore Forest Park in County Down.