Mark Butler says the federal government does not have the financial capacity to continue funding what were intended as emergency payments, and which came to an end on June 30.
"We're going to have to start to moving towards more normal programs that support the Australian community and people have been on notice about that for some time," he told ABC radio on Friday.
Asked if people without sick leave entitlements were likely to go to work with COVID-19 if they did not have access to government support, Mr Butler said he "hoped not".
"We can't continue forever to fund from the budget the gaps in the labour market that exist," he said.
Yet the minister warned health authorities are expecting a third wave of Omicron cases, with re-infections likely due to a new variant.
Australians must get their booster as soon as possible to protect themselves, he said.
"Even if you caught COVID in that big summer wave, where millions of Australians caught (it), if you've only had two doses ... you are potentially susceptible to infection over coming months," he said.
Mr Butler will meet with state and territory health ministers on Friday, and managing the coronavirus will be high on the agenda.
Ministers will discuss ways for more vulnerable people with COVID-19 to get access to antiviral drugs.
Mr Butler said it was important to expand the use of the antivirals to help manage the pandemic.
"We're getting feedback from pharmacists, GPs and patients alike (and) I don't think that there's a great level of awareness about these treatments out in the community," he said.
"You have to have a plan for when you get notified of a positive COVID test so that you can contact your GP quickly (and) get a script for these antivirals."
As the government announced it would hold an inquiry into vaccine contracts, Acting Prime Minister Richard Marles said it was critical the country was prepared for further sub-variants of the virus.
"We do need to learn the lessons of the failures of the past, it's not like there's not going to be any examination," he told Sky News on Friday.
"But this is not about an inquiry into all of that, it's about how we can best place ourselves going forward."
LATEST 24-HOUR COVID-19 DATA:
Victoria: 8057 cases, 12 deaths, 472 in hospital with 23 in ICU
NSW: 10,930 cases, nine deaths, 1558 in hospital with 41 in ICU
Tasmania: 1303 cases, no deaths, 47 in hospital with four in ICU
Queensland: 5313 cases, six deaths, 587 in hospital with 14 in ICU.