To date, 42 people across the state have become infected with the virus. Most of those contracted it overseas.
Two of the NSW cases were infected in other parts of Australia.
Members of the community have been urged to protect themselves by health officials.
“NSW Health is urging the community, particularly gay, bisexual and other men who have sex with men (GBMSM), to continue to be vigilant for the symptoms of monkeypox following local transmission of the virus in NSW,” NSW Health said.
The virus is transmitted skin to skin but contact needs to be prolonged.
Symptoms commonly appear seven to 14 days after skin-to-skin contact with an infected person.
They can include rash or lesions on the genital area, headache, body aches and fever.
NSW Health warns transmission is also possible by respiratory droplets in the initial period and contact with clothing, linen or other contaminated items.
“It is important that people with these symptoms avoid close contact with others,” NSW Health Executive Director of Health Protection Richard Broome said.
“Including sexual activity, as condoms are not effective at preventing the transmission of monkeypox.”
For most people, symptoms stop after two to four weeks.
Basic painkillers can be used to lessen symptoms, and antiviral drugs can be used in serious cases.
Last week VIctorian authorities reported the monkeypox virus is spreading in Melbourne in the first widespread example of local transmission since the global outbreak began.