The vast majority of the cases — 874 — are in the southern state of Victoria, prompting several other Australian states and territories to quarantine schoolchildren returning home from Victoria for seven days.
Singapore's government posted a warning on its Web site advising people against nonessential travel to Victoria, along with the United States, Canada, Mexico, Chile and parts of Japan.
But Health Minister Nicola Roxon on Friday said health officials were not surprised by the rapid spread of the virus, and said it was likely to continue spreading throughout the southern hemisphere's winter months.
"This recent surge in cases was not unexpected, given the behavior of the disease that we've seen in other countries," she said.
Australia's defense department canceled its annual parade celebrating the Queen's birthday near the capital of Canberra on Saturday, after one of the cadets who was supposed to have marched in the parade tested positive for the virus. The cadet and others he came in contact with were placed in isolation.
The disease has spread to 69 countries. A vast majority of the nearly 22,000 cases reported so far have been mild, though 126 people have died as a result of the disease, mostly in Mexico.