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.

A multi-storey church hostel collapsed last September in Lagos killing 116 people, many of them South Africans.
The authorities said it had more floors than its foundation could hold.
"The church was culpable because of criminal negligence resulting in the death of the victims," coroner Oyetade Komolafe said at the inquest in Lagos.
Mr Komolafe said Mr Joshua's Synagogue, Church of All Nations (SCOAN), had not obtained proper approval before putting up the structure.
Those who built the hostel should also be investigated, he said.
Africa news updates
TB Joshua, referred to by his followers as a "prophet", had blamed last year's incident on a small plane which he said had been circling the building, a claim dismissed by the court.
Straight after the building collapsed, emergency teams complained that church officials had blocked access to the site.
The coroner also criticised the fact that the preacher had not appeared as a witness during the inquest.
"Among the individuals and organisations summoned, only Prophet TB Joshua refused to testify," the AFP news agency quotes Mr Komolafe as saying.
The BBC's Will Ross in Lagos says the preacher went to another court arguing that the coroner did not have the right to summon him.
Mr Joshua's services, at a mega-church in Lagos's Ikotun district, are known for attracting thousands of people.
Followers in Nigeria and abroad believe he has the gifts of healing and prophecy.
Our correspondent says the coroner's verdict is really a recommendation and now it will now be up to Lagos state's director of public prosecutions to decide what legal action to take.
Profile: Nigerian preacher TB Joshua
In pictures: TB Joshua's ministry in 2005
There has been a squirrel pox virus outbreak among red squirrels at Tollymore Forest Park in County Down.
[NEXT_CONCEPT]
A church run by the popular Nigerian evangelist TB Joshua should be prosecuted after the collapse of one of its buildings, a coroner has ruled.