"The virus is among us, now we have do our utmost that it does not spread further. Too many are infected and if this goes on hospitals will collapse," Daniel Koch, head of infectious diseases at the federal health agency, told SRF radio.
Switzerland mobilized up to 8,000 members of the military on Monday and banned all public and private events after declaring the coronavirus outbreak an "exceptional" emergency that demanded more radical measures.
More than 2,330 people have tested positive for coronavirus so far in Switzerland, and at least 14 people have died.
Koch defended the government's policy to focus testing on people most at risk from the new virus and those who might need hospitalization.
Bottlenecks in processing test results were an issue, he said. Authorities were already running more than 2,000 tests a day.
"We will do more testing in Switzerland as soon as we can but the virus doesn't wait for it to be tested. Hospitals are seeing a leap in sick people and that is an alarm signal."
Makers of ventilators needed to help people in respiratory distress breathe have said that even Switzerland may not have sufficient equipment, should hospitals become overloaded with a deluge of patients.
The World Health Organization called on all countries on Monday to ramp up their testing programs as the best way to slow the advance of the pandemic.