The strong demand is straining the state's testing system, with long lines forming at Melbourne sites on Monday morning.

At least 10 testing sites across the city were temporarily shut at 9am after reaching capacity.

They included Alfred Health in the CBD, Montague Street in South Melbourne, Moonee Valley Racecourse, St Vincent's Hospital in Fitzroy and La Trobe University's Bundoora campus.

Monash University's drive-through at Clayton has reopened but others joined the list after midday.

A long queue was also seen outside the Bourke St walk-in site, with people at one point facing a wait of three hours to get tested before it closed as well.

Estimated wait times at other sites ranged from two hours to 15 minutes.

Victorian MP Ben Carroll said Acting Premier James Merlino and Health Minister Martin Foley were working "around the clock" to find solutions to cope with the influx of people needing tests.

"They are looking at more resources in terms of extending hours," he told reporters on Monday.

"It's only natural for Victorians, before they get together to see family at Christmas time, they want to get tested and have that peace of mind that they're COVID-free."

The state government has increased testing capacity by about 55 per cent since October, with around 260 sites now operating across Victoria.

But opposition health spokeswoman Georgie Crozier said the system was under "huge stress" because the government's failure to plan for Christmas.

"They've had months to plan for this," she said.

After another lockdown-plagued year, Victoria's health department has advised people not to go to Christmas gatherings if they have symptoms, wear masks when talking to others face-to-face and keep them short and outdoors.

"We encourage everybody to come back together for Christmas. But be sensible about it," Mr Carroll said.

Victoria reported 1302 new COVID-19 cases and zero deaths on Monday - the state's first day without adding a COVID-related fatality since September 16.

A further 13 Omicron cases have been discovered, taking Victoria's total to 37. Of those infections, 23 were acquired overseas and 14 in Australia.

A total of 406 patients are in hospital, 81 of whom are actively infected with the virus in intensive care and 43 on ventilators.

The seven-day hospitalisation average has risen by seven to 387.

Some 71,491 tests were processed in the 24 hours to midnight, while 4844 people were vaccinated in state-run hubs.

A pop-up COVID-19 vaccination van set up at Victoria's State Library on Monday and will operate until 6pm on Tuesday as part of a two-day booster shot blitz.

Australian Associated Press