The news comes as the state records one new locally acquired case and eight cases in hotel quarantine.
Jeroen Weimar said the state has already reduced its first dose allocation by about 30,000 this week in order to accommodate an increased number of second doses.
He said about 90,000 Victorians were receiving Pfizer vaccines through the state-run program until about a week ago.
But Mr Weimar said administrators would have to "ramp down" the rollout to about 40,000 first doses from the start of July due to a lack of supplies from the Commonwealth, a reduction which could continue into August.
"We are all frustrated that there is not more vaccine around," Mr Weimar told reporters on Monday.
Mr Weimar said the state had the infrastructure and capacity to administer more shots, and said about half of all adults in Victoria are now eligible for the jab.
The supplies are expected to increase again towards the end of the year in what the Acting Premier James Merlino described as a "mad rush".
Based on numbers from Commonwealth authorities, the state can forecast vaccine supplies 4-6 weeks ahead of time.
Mr Merlino told reporters he wants to see a sense of urgency regarding the vaccination rollout emerge from Monday's National Cabinet meeting.
"When you compare how Australia is going with the rest of the world, we are falling so far behind it's not funny," he said.
Victoria's new local case is a primary close contact that has already been linked to the current outbreak that sparked the latest statewide lockdown.
Eight more cases were also recorded in hotel quarantine, which Mr Weimar said included a group of six travellers who all tested positive on their first day in quarantine.
Mr Merlino acknowledged the hotel quarantine numbers were high on Monday but said he had not been advised to alter the current arrangements.
"There's no advice to change any of our arrangements in terms of returned travellers and our hotel quarantine system," he said.
Meanwhile the state's health authorities have tightened restrictions for travellers from NSW amid an outbreak there.
The health department added the local government areas of Bayside, Canada Bay, Inner West and Randwick to its list of orange zones on Sunday evening.
Anyone travelling to Victoria from these areas must get a COVID test and isolate until they receive a negative result.
The City of Sydney, Waverley and Woollahra LGAs have already been listed as orange zones.
More than 16,000 coronavirus test results were received in the 24 hours to midnight on Sunday, and the number of exposure sites remains at 108.