Dr. Judy Persichilli made the announcement during a press briefing on Friday afternoon.
One of the cases is a man in his 60s from Ocean County. The man developed symptoms on December 29 but he has since recovered.
The man had no travel history or clear exposure to others who were ill, Persichilli said.
VIDEO: Dr. Fauci on COVID-19 variants around the world
Fauci explains impact of COVID-19 variants on vaccine: 'We're paying very close attention to it'
The second case involved a child who stayed in northern New Jersey and has a history of traveling.
The child tested positive in New York earlier this month, Persichilli said, and state officials are working with their New York counterparts on tracing contacts.
A health official in the United Kingdom said Friday that there is some evidence that the new strain carries a higher risk of death, but stressed that the data is uncertain.
Scientists have previously said that the UK strain appears to be more contagious.
Meanwhile, Gov. Phil Murphy announced Friday that the state has administered more than 500,000 vaccines in about a month.
Murphy urged patience, since nearly 2 million residents already preregistered for the vaccine.
Starting Monday, New Jersey residents can call 855-568-0545 for assistance.