About 2,000 primary and secondary schools will close until 6 April to stop it spreading.
Officials in Hong Kong are also spending two days disinfecting the streets and housing estates.
The bug affects the way you breathe and has been called SARS - Severe Acute Respiratory Syndrome.
The outbreak has killed more than 50 people worldwide, with 1,500 showing signs of the virus.
On Sunday, Hong Kong officials said 60 more people had been infected. More than half of the new infections are in one block of flats.
Bit like a cold
At first no one knew what caused the bug which was spotted in Hong Kong in February.
Now doctors think it's similar to a type of virus called Corona which is a bit like the common cold - only more dangerous.
But the more they know about it, the easier it will be to treat.