The UAE's state-run WAM news agency made the announcement citing the Health and Prevention Ministry , but offered no details on where the stricken family lived nor where they were receiving treatment.
It also did not offer a number of those afflicted by the virus, other than to say the cases came from "members of a family arriving from the Chinese city of Wuhan."
The UAE is home to long-haul carriers Emirates and Etihad Airways and is a hub for global air travel.
Officials are taking "all the necessary precautions in accordance with the scientific recommendations, conditions and standards approved by the World Health Organization," the ministry said. "The general health condition is not a cause for concern."
The new type of coronavirus first appeared in the central Chinese city of Wuhan in December. Its symptoms, including cough and fever and in severe cases pneumonia, are similar to many other illnesses.
The new virus causes flu-like symptoms, such as fever, cough and in severe cases pneumonia. It's from the coronavirus family, which includes those that can cause the common cold as well as more serious illnesses such as SARS and MERS.
The viral outbreak that began in China has infected more than 6,000 people in the mainland and more than a dozen other countries. China's death toll has passed 100.