Mr Andrews said the grants would allow GPs and pharmacies to operate additional hours, hire more staff or rent out space to run their own vaccination hubs.
"For a relatively modest investment, we get a huge return. More and more people vaccinated means less people in hospital, our community and economy open sooner," Mr Andrews said.
Expressions of interest for the grants will open this week, with the funding to be distributed from 4 October.
Melbourne's lockdown will remain in place until 70 per cent of Victorians aged over 16 are double-vaccinated, which is forecast for 26 October.
A more significant easing of restrictions will occur when the 80 per cent double-dose target is met, forecast for 5 November.
Mr Andrews said the state was looking at shortening the interval between first and second doses of Pfizer vaccines at vaccination hubs, which is currently set at six weeks, but needed certainty on supply from the federal government before doing so.
"If we can get that certainty of vaccine supply then we may be able to bring those forward and that would help us reach 70 per cent double-dose faster and in turn, 80 per cent double-dose faster as well," he said.
Victoria recorded 705 new locally acquired cases on Monday and one death, a man in his 70s from the local government area of Darebin.
It brings the toll from the current outbreak to 25.
Mr Andrews said more than 80 per cent of the new infections were aged under 50, with a quarter aged in their 20s.
The new infections bring the number of active cases in the state to 8,538, including 363 people in hospital and 75 in intensive care, of whom 56 are on a ventilator.
More than 78 per cent of Victorians aged 16 and over have now had at least one dose of a COVID-19 vaccine, while 47.7 per cent have had two doses.
It comes as restrictions will ease slightly across the state on Wednesday, with Victoria expected to pass 80 per cent single-dose vaccination coverage on Tuesday.
Residents of locked-down areas will be able to travel 15km from home, up from 10km, while patron caps in regional venues will increase from 20 to 30.
Golf, tennis and cricket, as well as group personal training for up to five fully vaccinated adults, can also resume.
There was also good news for the city of Geelong, which was released from lockdown overnight, despite the diagnosis of six new cases on Saturday.
All cases were linked.